With Ferland Mendy still injured, most reports have pointed to Fran García as the leading candidate to leave this summer.
However, according to journalist Carlos Carpio, no final decision has been made.
Sources at the club have not ruled out Álvaro Carreras, 23, being the one to leave instead, with the full-back having fallen short of expectations in his first season, both on and off the pitch.
Club officials at the Santiago Bernabéu are clear that they will sanction a sale of Carreras if a suitable offer arrives.
"(Jose) Mourinho has reports on Álvaro Carreras saying he could have given more, on and off the pitch — if they offer €45 million for him, they'll sell him. His conduct wasn't what's expected of a Real Madrid player, he had run-ins with (Alvaro) Arbeloa," a club source explained in a conversation with Rubén Martín.
Carreras, for his part, is not giving up.
"He's motivated to turn his situation around, because they committed to him for five seasons. That's been the case since he joined the club and paid a significant fee for a full international," it was added.
The final outcome will depend on the offers Real Madrid receive this summer, with one of Carreras or García expected to leave the club.