Former Valencia sporting director Fernando Gomez says the club have discussed signing Dani Ceballos, but warned they must sell before they buy.
A bright start at the Emirates was dampened by injuries, although Ceballos has expressed his joy about playing under new manager Mikel Arteta.
Real are open to keeping the Spain international, but he will remain on the transfer list, according to AS.
Ceballos confirmed himself about interest from Valencia in January.
Speaking to El Chiringuito de Jugones, he said: "Yes, my agent told me about the interest of other teams but I did not play because I was coming back from injury.
"I started training and changed my situation. In the last month-and-a-half I felt important. I knew about Valencia's interest."
And while Fernando says the move would be a good idea for both parties, he warned Los Che would have to sell a midfielder first before buying the 23-year-old.
He told Tribalfootball.com: "This possibility has been discussed. I think Ceballos could fit with VCF, and especially into the 126.96.36.199 system that Celades likes so much. Besides, he knows the Andalusian player well.
"But in my opinion, if there are no players leaving this summer, there are too many in his position."