The Ivorian, who has played for the French side over 100 times, is reportedly a target for the Hammers this summer.
Manuel Pellegrini has shown a lot of ambition so far in the transfer market, having broken the club's record fee for Toulouse defender Issa Diop and signing goalkeeper Lukasz Fabianski from Swansea.
Seri has attracted interest from a variety of clubs such as Arsenal and Manchester City, and West Ham are suggested to be the latest to want to sign the £35 million-rated player.
It is understood that the midfielder would ideally like a move to the English game, but that has not stopped Italian side Napoli from also throwing their hat in the ring for his signing.
West Ham would certainly have achieved a coup if they manage to attract Seri to the London Stadium, with Chilean manager Pellegrini wanting to make his side challenge for the European football positions in next season's Premier League.