According to Bild (via the Metro), Alonso is on the shortlist to replace Ancelotti if the Italian leaves Real in the summer.
The Spaniard was appointed Bayer Leverkusen manager back in October, with the club sitting 17th in the table having won one of the first eight league matches.
Alonso has since guided Leverkusen to nine wins in 16 outings, helping them to ninth in the Bundesliga. Indeed, if the season had started when he was hired, Leverkusen would be fourth in the table.
Bild have also claimed Thomas Tuchel is very keen on the Real job, with the German currently learning Spanish.
Tuchel has been out of work since being sacked by Chelsea in September, less that two years into his tenure at Stamford Bridge.
There, the 49-year-old claimed the Champions League, UEFA Super Cup and Club World Cup while the Blues also made the FA Cup and Carabao Cup finals.
Mauricio Pochettino and Raul have also been touted as candidates for the Real job.