The 29-year-old spent last season on loan in his homeland with Deportivo, but any hopes of that deal made permanent were ended when the club were relegated from LaLiga at the end of the season.
Perez joined Arsenal from Deportivo back in 2016, costing the club £17.1m, but he failed to truly establish himself at the Emirates.
Should the deal be comeplted, Perez will become Manuel Pellegrini's ninth signing of the summer and will provide competition for main striker Javier Hernandez and Marko Arnautovic, with Jordan Hugill expected to return to hometown club Middlesbrough.
West Ham get their new Premier League campaign underway on Sunday when they take on Liverpool at Anfield in the early kick-off.