The midfielder is regarded as one of the top prospects in world football and Real recently moved to hand the player a long-term deal at the Bernabeu which does not expire until 2023.
However, after making just four starts in all competitions during the past two months, the 21-year-old has allegedly started to contemplate whether he wants to remain at the La Liga giants.
According to Diario Gol, the Spanish playmaker holds a desire to play in England and would like to play for United at some stage in his career.
The report also claims that boss Zinedine Zidane would be open to selling Asensio, who would command a sizeable transfer fee given his potential and release clause in his contract.
In total this season, Asensio has contributed four goals in 10 starts and eight substitute outings in La Liga and the Champions League.