The Morocco international is being tracked by a number of Premier League sides with Arsenal and Sunderland confirming their interest and Blackburn also said to be monitoring the situation.
Chamakh has made no secret of his desire to leave the French champions this summer, but as yet no deal has been agreed for his departure.
Les Girondins chairman Jean-Louis Triaud claims the Hammers have tabled one 5million euros offer for the striker, which was immediately turned down.
Triaud told L'Equipe: "That offer was not acceptable. So it was no. Moreover it is not obvious the player wants to join West Ham."
Reports in the French press claim West Ham could now return with an improved offer for the 25-year-old.
Gianfranco Zola has made no secret of his desire to improve his forward options with Luis Boa Morte ruled out until January with a serious knee injury.