The 22-year-old, who was billed as one of the best youngsters in Europe, has failed to impress for Los Blancos so far this season, as new boss Julen Lopetegui undergoes a baptism of fire.
Many expected him to flourish this season and step into the void vacated by Cristiano Ronaldo leaving to join Juventus.
But according to Spanish newspaper Marca, if a club were to meet the £100million asking price, the Spaniard could well be sold.
Chelsea and French champs Paris Saint-Germain are believed to be monitoring the situation.
Liverpool and Manchester United have also previously sniffed around the Bernabeu, and it would be no surprise if there was a scramble for his signature in January.
But while the club may be prepared to allow the talent to leave, the player himself might be less keen.
SunSport reported last month how Asensio insists he has never wanted to leave the club.
Asensio said: "I've never had the intention to go anywhere.
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