The Spaniard only made the move from Depor to the Emirates Stadium last summer but has struggled in England, making 21 appearances and scoring seven times in all competitions.
Having been left out of the Gunners' recent tour of Australia and China, Perez would appear to be surplus to requirements and looks almost certain to leave this summer.
Sevilla had been linked with a move but it is Deportivo who have lodged the only official bid, tabling an offer worth 10million euros.
The 28-year-old is eager to move back to the Riazor and end his nightmare in north London, claiming he has been badly treated by the club and Wenger, who he has accused of lying to him about his first-team opportunities.
"I feel cheated," Perez told La Voz De Galicia. "In February I was not allowed to leave for a move to China with the promise that I would play more and after that I had even fewer opportunities.
"But the shirt number is an ugly gesture (new signing Alexandre Lacazette was given his number 9 shirt). On our pre-season trip, Lacazette asked the boss and he accepted. I was only told afterwards.
"Last year he (Wenger) told me that he understood why I was upset. I think this season things will get worse, so help me out.
"Arsenal are not behaving well with me. To take the shirt number without telling me and to give it to a companion - it seems to me that it is the last straw.
"I can't continue this way. I have given everything but that has not been reciprocated, so I can't stand it any longer. I want to leave and be happy."