The Spanish giants are reportedly keen to bring their former midfielder back to the club.
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Ancelotti is out of contract at the end of this season and could depart after a three-year long second stint in charge.
He is understood to have agreed to take over the Brazilian national team in 2024.
As a result, Real Madrid are already working to bring in a replacement, with Alonso top of their list, according to the Mirror.
Alonso previously spent time as a youth coach in the Spanish capital after ending his playing career.
He also made 236 appearances and won six major trophies for Los Blancos.
After a spell in charge of Real Sociedad B, Alonso was appointed by Bayer Leverkusen in October 2022.
Having taken over with the club second bottom of the Bundesliga, he guided his side to a sixth place finish.
Leverkusen have since made an unbeaten start to this season, winning 11 of their 12 league matches to top the table ahead of Bayern Munich.
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Alonso’s success in the dugout has caught the eye, with Manchester City and Liverpool also said to be keeping tabs.
Both Liverpool and Real Madrid have the advantage of a special clause in Alonso’s contract which becomes active next summer.
Along with Bayern Munich, they are the only clubs who can trigger the release clause in his deal, which runs until 2026.
Alonso played for all three clubs, winning the Champions League with Liverpool in 2005.
He was also a part of a Spain team which won the Euros twice and the World Cup between 2008 and 2012.