Last summer, the Premier League outfit paid £17.1m to sign the Spaniard from Deportivo, but he went on to make just two starts in the league, with a further nine appearances coming from the bench.
Perez had already been expected to move elsewhere but his shirt number has now been given to new signing Alexandre Lacazette, and as well as a failure to gain regular first-team action, Perez has said that he feels "cheated" by manager Arsene Wenger.
The 28-year-old is quoted by La Voz de Galicia as saying: "I want to leave to play and be happy. Last year I barely had any opportunities and when I had them I took advantage of them and this season is clearly going to be more of the same. I want to fight to go to the national team. I want to play football, but for that I have to leave.
"I think that the best place for me is at home, with Depor. [Arsenal] are not behaving well with me. The thing of taking the shirt number without telling me to give it to a companion, it seems to me the last straw.
"I can not continue this way. I have given everything, but that has not been reciprocated, so I can't stand it any longer. I feel cheated. In February I was not allowed to leave for China with the promise that I would play more and after that I had even fewer opportunities."
Perez was not included in Arsenal's squad for their pre-season tour of Australia and China.