The Italian is known to be a big fan of the former Tottenham favourite.
The former Spurs star has been continuously linked with a return to the Premier League this season, in sources such as the Mail, having struggled to hit the strong form he managed in his debut season in Spain.
Manchester United and Chelsea have been particularly closely linked to the 25-year-old in recent weeks, even though both clubs have signed big name wingers in 2015, with United announcing a deal to sign Memphis Depay on Friday and Jose Mourinho bringing Juan Cuadrado to Stamford Bridge in January.
Bale, who has 17 goals to his name in 45 matches this season, down from the 22 he managed last year in a similar amount of games, had a disappointing game as Real slipped to a 2-1 win against Juventus in the firs leg of their Champions League semi-final.
There was much criticism of the winger in both the UK and Spanish media, leading to renewed reports that Real may be prepared to cash in on the player just two years after they paid a reported world record fee to bring him to Madrid.
The Mail report that Ancelotti, who himself may have to win the Champions League in order to remain at Real, has told Los Blancos president Florentino Perez that Bale should not be considered for transfer under any circumstances.
While the former Stamford Bridge boss is in charge, it looks like any designs United or Chelsea may have to bring Bale back to the UK could be difficult, but if the Italian is cast aside, expect to see renewed and increased speculation of a Premier League return.