Perez has found first-team football hard to come by since joining the north Londoners two years ago from Deportivo La Coruna for £17million.
The Spaniard returned to the Riazor on loan last season but failed to impress as Depor were relegated to the Segunda Division.
Perez is keen to stay and fight for his place in Unai Emery’s side this season but faces a stern task to get ahead of Pierre-Emerick Aubameyang and Alexandre Lacezette in the pecking order.
And according to Lovelle, West Ham have made a bid to end Perez’s nightmare stay at the Emirates.
“I know that West Ham want him and they have made an offer,” Lovelle told ESPN FC.
“It is an option. Lucas is happy at Arsenal but he wants to play regularly and West Ham is an option for him.”
Lovelle revealed the Hammers’ interest in acquiring his client’s services earlier this week, telling CalcioMercato: “West Ham is an option, he might leave [Arsenal].
“West Ham keeps him in London and in the Premier League, and they are a great club.”
It has been claimed that Perez is keen to seal a move to the London Stadium as soon as possible, with the Evening Standard reporting that the 29-year-old is hopeful of joining Manuel Pellegrini’s side by the end of the day.
Should Perez leave Arsenal, he’ll do so with a record of seven goals in 21 games.
And only two of those appearances came in the form of starts as he often found himself playing second fiddle to former Gunner Olivier Giroud.
Arsenal kick off their Premier League season on Sunday with a home game against champions Manchester City.
West Ham, meanwhile, begin their campaign with a trip to Anfield to face Liverpool.