The Christmas break looks like it came at a bad time for Real Madrid this season as their form following the pause in their campaign has been shaky at best.

Carlo Ancelotti and the Real Madrid hierarchy may well be already plotting to improve their squad in the summer to give them the best chance of being successful next season. And here are 10 players who could be on their shortlist for the next transfer window.

David De Gea (Manchester United)

Manchester United goalkeeper David De Gea has established himself as one of the best ‘keepers in the world in recent seasons. When he initially moved to the Premier League from Atletico Madrid, he had a shaky start to his career at Old Trafford. However, Sir Alex Ferguson stuck with the Spaniard and he eventually reaped the same rewards in which Louis van Gaal is enjoying this season.

The summer could be the right time for Real to make a move for the United shot-stopper to try and secure him as their number one ‘keeper ahead of the aging Iker Casillas and Chilean Keylor Navas, who has not made a big impact at the club since signing last August from Levante.

De Gea has been linked with a return to Spain and a move to Real over the past couple of months, so it is likely there could be some interest in the story. He is now the first-choice ‘keeper for the national team and there are not many that are rated better anywhere in the world right now.

United don’t look to be any closer in winning the Premier League, where they are 150/1 with betfair at the time of writing, but they may qualify for the Champions League next season. De Gea will have to decide whether to upset fans of his former club Atletico Madrid by signing for their bitter rivals if they do decide to make a move for him later this year.

Edinson Cavani (PSG)

Uruguay 3 - Argentina 2 |

It looked like Cavani was set to leave Paris in January but a move away from the French champions never materialised.

Since the winter break, Cavani has performed like a player who has something to prove. It may be the case that PSG forward wants to verify his worth to manager Laurent Blanc or he could be playing to attract the attention of some of the other big clubs in Europe, including Real Madrid.

If Cavani was available on the transfer market this summer, Real could do much worse than acquire his services. Although they have plenty of competition already in that department, he is very different to some of their attacking options in their squad.

The PSG forward is a strong presence in the final third of the pitch and can be played out wide if required. As the most expensive player in French football, he would not come cheap so Real would be one of the few clubs who could afford his services.

Cavani may see the summer as the perfect opportunity to pick up a fresh challenge in his career. PSG look on course to win Ligue 1 again but Chelsea are favourites to get past them in the last 16 of the Champions League. In his three years with the French side, they have not come close to winning Europe’s premier competition.

Thiago Silva (PSG)

Top quality defenders seem hard to come by at the moment in Europe but one of the most consistent players on the continent is PSG’s Thiago Silva.

Although the Brazilian did not shine at the World Cup with his national team, who were thrashed 7-1 in the semi-final of the competition in their home country, Silva’s reputation still remains intact as a top class centre-half.

At the age of 30, the PSG defender is probably at his peak and has three to four seasons in him at the highest level. He has played football in Italy for Milan, Russia with Dynamo Moscow and a number of clubs in his homeland of Brazil, so he has a range of experience in different countries.

Although Silva is settled in France at PSG as their captain, he may find it hard to turn down the call of Real Madrid in what is likely to be his last chance to move to one of the five biggest clubs in the world.

Ancelotti worked with Silva at Milan and at PSG so knows the player well. The Italian purchased him from Brazilian club Fluminense when he was in charge of Milan, while he also went out and bought the defender when he was manager of PSG.

Carlos Tevez (Juventus)

tevez  There are not many strikers in Europe with a better goalscoring record than Carlos Tevez at the moment. In what is now his sixth club at Juventus, the Argentinian has scored 33 goals in 54 appearances for the Italian giants.

Tevez first made his name in England when he signed for West Ham in what proved to be a controversial move due to being owned by a third party. Manchester United bought the full rights for the striker after his first season with the Hammers and he helped them win the Premier League twice and the Champions League in 2008.

In Cristiano Ronaldo, Gareth Bale and James Rodriguez, Real Madrid have three of the best attacking players in the world. However, neither of them are natural number nines who prefer playing as a traditional striker.

Tevez would give Ancelotti a different option at the front of the pitch and, with some of the best players in the world around him, it would be a huge surprise if he did not score lots of goals in this Real side.

Surprisingly, Tevez was not included in the 23-man squad for Argentina at the World Cup last year. If he is looking for a return to the national team, scoring goals for Real Madrid would surely help him to pick up a recall back into the squad.

Sergio Aguero (Manchester City)

Like David De Gea, Sergio Aguero signing for Real Madrid would not go down very well with Atletico fans. However, the Manchester City forward has earned the opportunity to play for the Spanish giants and have the chance to win the Champions League with one of the main contenders in the competition.

City look like they are going to finish second in the Premier League to Chelsea this season and it could well end up being a trophyless campaign for Manuel Pellegrini’s side. If that is the case, it may just tempt Aguero to move in the summer.

Real would surely be in the mix to sign the Argentine international if they believed there was a slim chance of the City man being available. He is regarded as one of the best players to participate in the Premier League and has arguably been City’s best ever signing since they came into money through their relatively new owners.

The only thing which may put Real off signing Aguero is his injury record in recent seasons. He has succumbed to a number of injuries over the past couple of years so they may have to bear in mind that the chances are they will not get a full season out of him.

Mats Hummels (Dortmund)

It looks certain that Mats Hummels’ time at Borussia Dortmund will be over at the end of the season. The former German champions are struggling at the wrong end of the table in the 2014/15 campaign as it looks as though the sale of a number of their star players has taken its toll on the club.

Hummels was a huge part of Germany’s success in Brazil as he gave them a solid platform at the back to work around.

There is certainly going to be lots of competition for the centre-back’s signature later this year but Real Madrid will be able to offer him Champions League football once again and the opportunity to be in contention for domestic and European trophies.

Real’s back four has come in for a lot of criticism so far this season and is considered the weakest area of the side. It will no doubt be a priority of Ancelotti’s this summer to try and improve his defensive line to stop his team leaking goals.

Julian Draxler (Schalke)

Twenty-one-year old Julian Draxler’s reputation is growing with each year. The Schalke winger has already picked up 15 caps for his national team of Germany and could be at the centre of a bidding war this summer when he is expected to leave his current club.

The youngster has made more than 100 senior appearances for Schalke since breaking into the first team in 2011.

Draxler would bring a lot to Ancelotti’s squad as he is quick, strong and scores plenty of goals from his position out on the wing.

Although the German is a childhood fan of Schalke, it would surely be very difficult for him to turn down Real Madrid, where he would join up with his international team-mates Toni Kroos and Sami Khedira.

Real Madrid are not short of midfield players but since they let go of Angel Di Maria to Manchester United, they don’t have many players with real pace in the wide positions.

Nolito (Celta Vigo)

Spaniard Nolito made a return to La Liga in 2013 when he signed for Celta Vigo from Benfica. The 28-year-old made a big impact at the Portuguese club which was enough to persuade then manger Luis Enrique to sign the former Barcelona forward.

In the last two seasons with Celta, Nolito has found the back of the net on 22 occasions, while also featuring prominently in the assists chart.

The Celta man was rewarded for his performance with his domestic club by picking up his first cap for Spain in November in a 1-0 defeat to world champions Germany in a friendly.

Although things did not work out with Barcelona in the early stages of his career, it is unlikely to put Real Madrid off purchasing the player this summer.

Ross Barkley (Everton)

Everton’s Ross Barkley is arguably England’s brightest young talent at the moment. He broke into the national team just before the World Cup in Brazil after some eye-catching performances in the Premier League for the Toffees.

With the greatest respect to Everton, they may struggle to keep a player of his talent in the long-term future, with a number of the big guns in England already monitoring the player.

It is not out of the question that a club like Real Madrid could take a chance on a player like Barkley. He would not lack the flair needed to play for the Spanish giants and if he continues to improve, he could end up being one of the Three Lions’ best players.

Comparisons have already been made with Paul Gascoigne and Wayne Rooney, who also started his career at Everton before moving onto Manchester United.

Not many English players make the move to Spain but Real did sign Welshman, Bale from Tottenham.

Marco Reus (Dortmund)

Marco Reus has been a big part of Dortmund’s success in Germany for Dortmund in recent years. He helped the club reach the final of the Champions League in 2013, while he lifted the DFL-Supercup in 2013 and 2014.

The problem Reus has had is that he is one of the few big name stars who remain with BVB. Many of his former teammates jumped ship to join Dortmund’s rivals Bayern Munich which has made it very difficult for Jurgen Klopp’s side to compete with the biggest club in Germany.

Reus would improve any side he joined in Europe as he is one of the most talented players in any league across the continent. Ancelotti would be able to play him as a winger, attacking midfielder or in a more advanced position.

The German has bags of experience in the Champions League and playing international football so the step up to Real Madrid, who have been linked with him, should not be a problem for the player.