The Spain international's existing deal at Bernabeu is due to expire at the end of June, and there has been a host of speculation surrounding his future over the last few months.
The 27-year-old has again found it difficult to secure regular starts this season, but he has been a regular for Los Blancos, scoring seven goals and registering five assists in 34 appearances.
According to journalist Carlos Carpio, it is now 'practically impossible' for Asensio to sign a new deal at the club, as the two parties are too far apart when it comes to wages.
The forward allegedly wants a €6m (£5.3m)-a-year deal, but Real Madrid are only said to be prepared to pay him €4m (£3.5m) a year, with neither party prepared to negotiate.
As a result, Asensio is set to depart on a free transfer this summer, with a host of clubs from England and Italy believed to be keeping a close eye on the developments.
Arsenal, Liverpool and Manchester United are thought to lead the Premier League interest, while AC Milan and Juventus are also being linked with his services.
Barcelona have also previously been credited with an interest, with the Catalan outfit believed to be considering offering the Spaniard the chance to complete what would be a shock move.
Asensio has been with Real Madrid since 2014, representing the club on 269 appearances in all competitions, contributing 56 goals and 29 assists in the process.
Speaking last month, Los Blancos boss Ancelotti admitted that he was unsure whether the Spaniard would be penning a new deal at the club.
"He is looking sharp. I don't yet know if he's going to stay or not. He has a contract and I'm not overly concerned because we have some very important challenges this season and he is contributing. He will make the right decision together with the club," said the Italian at the time.
Asensio has scored five goals and registered three assists in 20 La Liga appearances this season.
Meanwhile, he has contributed two goals and one assist in eight Champions League outings, with the club looking to defend the European Cup this term.
Karim Benzema, Toni Kroos, Dani Ceballos, Luka Modric, Nacho and Mariano Diaz also only have deals with Real Madrid until the end of June.