BBC Sport have reported that PSG are not willing to lose the Italian, who has a year remaining on his current contract.
It’s been a far from successful season for Real Madrid, who end the 2012/13 campaign without silverware.
Here we look at five potential Ancelotti targets, if he gets a move to the Bernabeu.
Borussia Dortmund's Ilkay Gundogan.
High on Real Madrid’s priority list will be a midfielder to replace Xabi Alonso. Step forward Ilkay Gundogan.
The 22-year-old is one of Borussia Dortmund’s key players. Primarily a defensive midfielder, his attacking abilities are first-class, he has a tireless work rate and his passing is one of the best aspects of his game.
Alonso, who has been one of Madrid’s most influential players since joining the club from Liverpool back in 2009, is nearing the age of 32 and has rejected an extension to his current contract, according to the Daily Mail.
PSG forward Zlatan Ibrahimovic.
Zlatan Ibrahimovic and Ancelotti are fresh from winning the Ligue 1 title together with Paris Saint-Germain.
With Gonzalo Higuain reportedly leaving the Bernabeu, according to the Daily Mail, and Karim Benzema proving too inconsistent in front of goal, Real Madrid will need a striker.
Who better, then, than Ibra—the 6'5" powerhouse who has 29 goals and nine assists to his name in Ligue 1 this season.
"I have a fantastic relationship with Ancelotti and I don't want him to leave the club." Ibrahimovic was quoted on Goal.com.
Perhaps the Swedish striker, who has played for seven clubs in his career so far, will follow Ancelotti to La Liga.
Tottenham Hotspur's Gareth Bale.
Rumours of a Bale exit from White Hart Lane have mounted considerably since Spurs failed to qualify for the Champions League, with former Premier League defender and World Cup winner Marcel Desailly telling the BBC he thinks Bale should leave Tottenham.
Gareth Bale is a Real Madrid-quality signing. He has had an exceptional season. He can punish any team in the world and has the footballing qualities we look for in Madrid.
However, it has been reported in The Guardian that Bale will sign a new contract with Spurs.
Elsewhere, speculation suggests that Madrid president Florentino Perez is determined to sign the Welshman this summer, as reported by the Daily Star.
Real Madrid love to spend, and they have the funds to afford big names. But what if they gave their young players a chance and brought loanees back into the fold?
Take Daniel Carvajal, for example, who came through the Real Madrid youth system and was sold to Bayer Leverkusen last summer.
The highly rated 21-year-old, who plays as a right-back, has a clause in his contract that allows Madrid to buy him back this summer for a fee in the region of €6.5 million.
Carvajal has played 32 matches for the Bundesliga side this season, scoring once and registering eight assists. The Spain U21 man would be a good replacement for the 30-year-old Alvaro Arbeloa.
There are other "Canteras" who could be trusted to break into the side—like Nacho Fernandez, who could take over from 30-year-old Pepe in central defence. Juanfran, a right winger who has already made his debut for the first team, could take over from Angel Di Maria. And Jese, a classic No.10 who has already been courted by Tottenham Hotspur, according to Metro.
Ancelotti may have to buy new talent for the Bernabeu stage, but some of it is already waiting in the wings.
The 21-year-old is an attacking midfielder and could be an ideal target if Ancelotti wants to find a suitable replacement for Cristiano Ronaldo, who could leave Madrid this summer.
Francisco Roman Alarcon Suarez has three years remaining on his current contract with Los Boquerones, but the club’s dire financial situation looks to be speeding up his early departure from La Rosaleda.
Real Madrid look like they are the front-runners in the battle for Isco's signature.
This week, Malaga director Francisco Aguilar confirmed interest from the Bernabeu, on Goal.com.
Isco is yet to confirm that any talks have taken place, telling Spanish TV station Cuatro (via Goal.com):
"We'll see, let's see what happens..."