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.

Two-time major winner McIlroy, 25, and Danish former world number one Wozniacki, 23, announced their engagement on New Year's Eve.
Media playback is not supported on this device
"The problem is mine," McIlroy said. "The wedding invitations issued at the weekend made me realise that I wasn't ready for all that marriage entails."
The couple had been together for more than two years.
McIlroy is currently at Wentworth for the BMW PGA Championship, the European Tour's flagship event which starts on Thursday.
Wozniacki is set to compete in the French Open in Paris starting on 25 May.
In a statement issued through his management company, McIlroy added: "There is no right way to end a relationship that has been so important to two people.
"I wish Caroline all the happiness she deserves and thank her for the great times we have had."
"The news has shocked the worlds of both golf and tennis, particularly with the timing of the split. McIlroy is due to start a crucial run of tournaments, while Wozniacki is playing the upcoming French Open."
Speaking at Wentworth on Wednesday, McIlroy said the decision to end the engagement had been mutual and amicable.
He said it was a difficult time, but that the move was best for both of them.
McIlroy won the US Open in 2011 and US PGA Championship the following year.
Wozniacki, who has reached the final of one grand slam tournament - the US Open in 2009 - is currently ranked 13th in the world.
When McIlroy announced their engagement, he tweeted: "I have a feeling it is going to be a great year."
Deportivo La Coruna have made an offer to re-sign Arsenal striker Lucas Perez, says the Spaniard's agent.
[NEXT_CONCEPT]
Northern Irish golf star Rory McIlroy has broken off his engagement with tennis player Caroline Wozniacki.