The Hammers are known to have made a move for the France international striker, but are yet to put a suitable bid on the table.
Talks remain in progress, though, and Avram Grant is determined to get his man.
Reports have suggested that the likes of Liverpool and Arsenal are also keen on the 23-year-old frontman, but they have yet to enter negotiations.
Stellardo has revealed that West Ham and Turkish giants Fenerbahce are the only clubs in the running at the moment, and has hinted that Remy would welcome a move to Upton Park.
"West Ham? Remy is definitely interested," he is quoted as saying on lequipe.fr. "Liverpool, Chelsea and Arsenal? I have heard about their interest but I have had no contact.
"The only clubs I have talked to are West Ham and Fenerbahce.
"Fenerbahce have also contacted Rennes about Asamoah Gyan and Lyon about Bafetimbi Gomis. If either of those players leave, it is not impossible that their clubs will turn to Loic as well."