Perez has been at the north London club since signing in 2016 for an estimated £17m, although the Spaniard has found it tough to become a regular at the Gunners, making only 21 appearances for the club and spending the 2017/18 season on loan at former side Deportivo la Coruna.
Despite his struggles in England, Perez's agent has confirmed in an interview with ESPN that his client has peaked the interest of the Hammers, with Manuel Pellegrini's side apparently making an offer to sign the forward.
Lovelle said: "I know that West Ham want him and they have made an offer. It is an option. Lucas is happy at Arsenal but he wants to play regularly and West Ham is an option for him.
"There are other clubs interested but joining West Ham would allow him to continue in London and in the Premier League and Lucas wants to continue in London."
Perez was part of new boss Unai Emery's squad that travelled to Singapore for pre-season, although recent developments suggest his time at the Emirates could be coming to an end.
ESPN reporter Eduardo Fdez-Abascal has stated via his official Twitter account that Perez is on the verge of moving to the Olympic Stadium, with him expected to undergo his medical ahead of signing a three-year deal worth an apparent £5m.
Perez would be the second player to swap Arsenal for West Ham this window should the expected deal go through, after Jack Wilshere joined on a free transfer following the expiration of his contract.