The 28-year-old joined Arsenal from Deportivo La Coruna last summer in a £17million deal but has made just two starts in the Premier League so far this season.
While West Ham have turned the corner in recent week, Slaven Bilic believes he lacks attacking options and sees Perez as an ideal acquisition.
The Times claim Bilic is a fan of the Spanish striker, who has scored six goals and created five in 21 outings so far for the Gunners this season, and the Hammers boss reckons the former Deportivo man could become available this summer, amid his lack of opportunities at Arsenal.
However, despite his lack of starts, Arsenal appear to want to keep Perez as they rejected a £26million offer in January from a Chinese Super League club. With this in mind, Bilic will know that the Spaniard will not come cheap, even if Arsene Wenger continues to leave him on the bench.
Perez has stated that he is happy at Arsenal and although a permanent move away from the Emirates seems unlikely to occur this summer, a loan may not be out of the question.