Deportivo admit they have next to no chance of re-signing Lucas Perez from Arsenal this summer.
Perez, a £17m signing from the La Liga club last year, is eager to move on this summer after a disappointing first season in English football where he found first-team opportunities difficult to come by.
The Spaniard was left out of Arsenal's pre-season tour squad for their trip to Australia and China and has seen his number nine shirt taken away from him and handed to new the club's new record signing Alexandre Lacazette.
The 28-year-old has already admitted he would be very interested in a return to Spain to play for Sevilla next season but Deportivo suggest that despite the arrival of Lacazette, Arsenal are still determined to hold onto the player.
"Lucas is at a great club who made a big financial effort for him, there is a high level there and also the desire of the club is not to look for an exit," Deportivo president Tino Fernandez said, ESPN report.
"We have spoken to Arsenal, we were interested and we informed them of that, although it is true 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."
Even with his circumstances changing in recent days, Fernandez still describes his side's chances of signing the Arsenal forward as "remote."
Perez's frustrating first season in England saw him start just nine times across all competitions and only twice in the Premier League.
Arsene Wenger was sympathetic over his plight at the end of last season, apologising for not giving him more regular first-team opportunities and insisting he would "love" to give him more opportunities next season.
"I would love to [keep Perez at Arsenal]," Wenger said at the end of last season. "If I am the manager, I would love to keep him. We would have to sit down together to see if he has a reasonable chance to play next season."
However, with Lacazette's arrival, Alexis Sanchez and Olivier Giroud possibility set to remain in north London and with Danny Welbeck also in the equation, Wenger may struggle to keep the player happy.