The Mali international only moved to Upton Park last summer, with the Hammers luring him away from Sochaux.
The 25-year-old may, however, be heading back to France after just 12 months in England.
Maiga struggled to hold down a regular role during his debut season at West Ham, preventing him from replicating the prolific form he had displayed in Ligue 1.
St Etienne would be willing to offer him a route out of East London, as they step up their search for a replacement for Pierre-Emerick Aubameyang - who has linked up with Borussia Dortmund.
"Maiga is a player we have studied," Romeyer told beINSPORT.
"Maiga is one of the options we have looked at, but there are other players. We will make a signing as soon as possible."