Each of the 25-year-old appearances this season have come from the substitutes' bench with five cameo outings totalling just 69 minutes.
With plenty of football still to be played, the playmaker has an opportunity to break into Carlo Ancelotti's rejuvenated side.
However, according to journalist Anton Meana, the Spain international may be prepared to formally request a transfer from the Bernabeu.
Speaking on El Larguero, Meana suggested that Asensio does not understand why he has been given such a role by the club's new manager.
Asensio has less than two years remaining on his contract, something which could force Real's hand in 2022.