The Canary Islands-born defender wants to stay and fight for his place, but the club, working alongside super-agent Jorge Mendes, is searching for a solution that suits all parties. Should his departure be completed successfully, it would prove significant in freeing up funds and squad space for Real Madrid to pursue the new centre-back Mourinho has requested for the coming season.
Asencio's fall down the pecking order follows the arrival of Ibrahima Konaté this summer, leaving him behind Éder Militão, Antonio Rüdiger, Dean Huijsen and Konaté himself in Mourinho's defensive plans.
According to Fabrizio Romano, the decision has been on the cards since Mourinho's return to the club in June, part of a wider defensive rebuild that has also brought in Marc Cucurella and Denzel Dumfries this summer.
Real Madrid have already offered Asencio to several European clubs through intermediaries, with RB Leipzig among those named as possible destinations, while Getafe and newly promoted Málaga have also been credited with interest domestically.
Despite his tender age and previous role as a first-team regular, Asencio's market value stands at a relatively modest €20 million, meaning any interested club would be expected to meet close to that figure to complete a deal.
Mourinho is understood to have identified a left-footed centre-back as his priority defensive target for the remainder of the window, with Inter Milan's Alessandro Bastoni among the names linked, and Asencio's departure viewed as a key step in freeing up the finances required to complete that signing before the transfer window closes.
Asencio broke into the first team during the 2023-24 season after injuries to David Alaba, Éder Militão and Dani Carvajal, and went on to earn a regular starting role under Carlo Ancelotti, even making his debut for the Spain national team.
He signed a contract extension to 2031 last year in recognition of that breakthrough, including the club's usual buy-out clause protecting against unwanted takeovers. That long-term commitment means any exit this summer would most likely take the form of a loan rather than a permanent transfer, allowing the club to retain a stake in his future.