Perez has failed to establish himself as a first-team regular since being signed from the Spanish club a year ago.
He is expected to leave the Emirates Stadium ahead of this month’s transfer deadline and a number of Spanish clubs have expressed an interest in signing him.
So too have Newcastle, with Magpies boss Rafael Benitez reportedly keen to take him to St James’ Park.
But Perez, who has made it clear he wants to leave Arsenal this summer, appears to be set for a return to Deportivo.
Lovelle told Sky Sports News: “I think the £10.9m that Deportivo have offered is a great deal. Deportivo received £12.7m when they sold him to them last summer.
“They are giving everything to make this transfer possible. Lucas wants to play but he has a contract with Arsenal. I am hopeful that an agreement can be reached.”
Perez managed just 11 Premier League appearances for Arsenal last season and scored one goal, with all but two of those outings coming as a substitute.
The 28-year-old made 10 appearances for the Gunners in other competition and scored six goals.