The 28-year-old moved to the Emirates Stadium last year from Depor for a reported €20million but he has struggled to force his way into manager Arsene Wenger's plans.
Perez was left off Arsenal's squad for their pre-season tour of Australia and China, prompting speculation of a move away from the club, with the player said to be eager for regular first-team football to bolster his chances of making Spain's World Cup squad next year.
However, Depor president Tino Fernandez says he has been told by the Gunners that they are not interested in a sale.
"Lucas is at a great club who made a big financial effort for him, there's a high level there and also the desire of the club is not to look for an exit," he said on Monday.
"We've spoken to Arsenal, we were interested and we informed them of that, although it's true that that was days ago and other things have happened since then, like the fact that he will not be with the team for a few games."
He added that "the possibilities are remote" that Perez will return to the Riazor.