The former Liverpool star and current Bayer Leverkusen boss has been linked with Los Blancos following their 3-1 derby day defeat to Atletico Madrid on Sunday.
It leaves Real Madrid third in the table, behind Barcelona and Girona.
But despite the rumours surrounding his possible replacement, former Everton and Chelsea manager Ancelotti has addressed the links by lauding ex-Real star Alonso, stating he hopes he returns to the club one day.
Ancelotti went on to name drop another ex-Liverpool and Real Madrid player to join him in the dugout, too.
Alvaro Arbeloa, who is Real's Under-19s boss, spent two years at Anfield between 2007-2009 before linking up with Real, who he stayed at until 2016.
READ MORE FOOTBALL NEWS
Iconic stadium left unrecognisable as demolition continues ahead of rebuild
Mikel Arteta confirms star man will miss Brentford clash and is doubt to face Bournemouth
Commenting on his ambitions for Real once he departs, Ancelotti said in his press conference on Tuesday: "Look, I've had Alonso, as a player.
"His knowledge of football is top level.
"He's doing great with Bayer Leverkusen because he does these readings.
"This ability, I wish him as well as Arbeloa and Raul, I really wish [for] them to coach at Real Madrid one day."
Most read in Football
Ratcliffe to revive Man United takeover, Sancho exiled, Newcastle's Barnes blow
Pochettino confirms co-owner Eghbali regularly enters Chelsea dressing room after games
Phil Jones confirms new plans after leaving Man United in summer
Jadon Sancho appears to deactivate Instagram page as Erik ten Hag row rumbles on
Ancelotti's deal is set to expire at the end of this season, marking three years since he returned to the Bernabeu for his second managerial spell.
But the 64-year-old has insisted he's not thinking about his future at the moment, despite his contract ticking down and the reports of former Real Madrid academy coach Alonso taking over.
He said: "Everyone knows I'm happy here. But this is not an important matter now.
"We will talk in the future, there's time".
Ancelotti has managed 243 games with Real Madrid, winning two Champions Leagues, one LaLiga title and two Spanish Cups.