Reports claim the Turkish club have agreed a deal with Paris Saint-Germain to sign Asensio and though personal terms still need to be agreed, they are now favourites for his signature.
Asensio scored eight goals in 21 appearances while on loan at Villa during the second half of last season and the club were initially keen to make the move permanent.
But Villa’s failure to qualify for the Champions League means they are having to work more shrewdly in the market, while a drop off in form over the final weeks of the campaign also posed questions over whether the Spain international was up to the physical demands of the Premier League.
Asensio, a three-time Champions League winner, failed to find the net in any of his last 11 appearances.
Unai Emery is keen to recruit a winger in the transfer window, while a right-sided centre-back is also high on the club’s agenda as they look to bring in cover and competition for Ezri Konsa.
Midfielder Enzo Barrenechea, meanwhile, has emerged as a possible target for Benfica. The Argentine, who spent the whole of last season on loan at Valencia after joining Villa from Juventus, is thought to have several suitors across Europe.