Perez, 28, joined the Gunners for £17.1m last summer after two seasons at Spanish side Deportivo.
He has made 21 appearances for Arsene Wenger's side in all competitions, scoring seven goals, but has not played since March.
"Arsenal know we want to go, that there are no opportunities here," said Rodrigo Fernandez Lovelle.
Lovelle said the uncapped Perez wanted to leave in order to get more playing time in an attempt to break into the Spain squad for the 2018 World Cup in Russia.
He added his client was "angry and sad and upset" that Arsenal had given the number nine shirt to new record signing Alexandre Lacazette without Perez "being asked".
Deportivo's offer is believed to be in excess of the reported £7.9m La Liga rivals Sevilla paid to sign Nolito from Manchester City.
"Deportivo made an offer a week ago - it is a permanent deal and worth more than Nolito's move to Sevilla," said Lovelle.
"Of course [he was told he would play more]. Lucas signed for Arsenal and was the happiest person in the world and with all of his dreams to fulfil.
"Every time he played he did well, but after every time he got fewer and fewer opportunities."
Perez suffered a thigh injury in March but was fit again before the end of the season, with Wenger saying in May that he felt "a bit sorry" for him.
"He's a top quality striker but I couldn't give him the games he wants and deserves," said the Frenchman.
Perez joined Deportivo on an initial season-long loan from Greek side PAOK in 2014 before signing a permanent deal in 2015.
Deportivo La Coruna have made an offer to re-sign Arsenal striker Lucas Perez, says the Spaniard's agent.