The Italian faces an uncertain future at the Santiago Bernabeu despite being under contract until the summer of 2026.
Ancelotti recently saw Real Madrid exit the Champions League at the hands of Arsenal, although Los Blancos could still finish the season with a domestic double.
Los Blancos are set to face Barcelona in Saturday's Copa del Rey final, while they are still in the hunt to retain the league title they won last season.
While Ancelotti could claim silverware in the closing stages of the season, there appears to be a strong possibility that the Real Madrid hierarchy could make a change in the dugout ahead of the 2025-26 season.
Laghari wants Klopp at Real Madrid
Bayer Leverkusen boss Xabi Alonso is regarded as one of the leading contenders to replace Ancelotti as Real Madrid head coach.
Former Liverpool manager Klopp is another name that has been mentioned, with The Telegraph reporting that an individual close to Florentino Perez wants to appoint the 57-year-old.
Laghari, who was regarded as a potential successor to Perez, has supposedly placed Klopp at the top of his managerial wishlist, although it is unclear how much influence he will have on the club's new appointment.
The Spanish banker has worked with Real Madrid via his role at Key Capital Partners, as well as being a founder of A22 Sports, the company that runs the European Super League project.
Klopp unlikely to accept Real Madrid job
However, Laghari would likely experience disappointment in his efforts to bring Klopp to the Santiago Bernabeu, with the ex-Liverpool manager content in his current role with Red Bull.
Klopp is head of global soccer for the drinks brand, which owns several clubs across the world, including RB Leipzig, New York Red Bulls and Red Bull Salzburg.
His job is said to suit his current lifestyle after giving up the demands of day-to-day football management when he left Liverpool at the end of last season.
As a result, Klopp will not consider any managerial roles until at least next summer, although it is unclear whether he will even resume his coaching career.
Written by
Ben Sully