Marouane Chamakh's agent has refused to rule out a late switch to West Ham, according to Sky Sports News.
The Moroccan striker has been linked with a move away from Bordeaux for much of the summer and a number of English clubs have expressed an interest.
Arsenal ended their pursuit after having an offer rejected, while Bordeaux boss Laurent Blanc was reluctant to do business with Sunderland.
The Hammers then entered the chase but a possible deal appeared to have collapsed towards the end of August.
Chamakh stressed that he would be prepared to stay at Bordeaux and revealed there was only a 10 per cent chance of him leaving at such a late stage in the transfer window.
However, West Ham could be set to make a last-ditch attempt to sign the 25-year-old as Gianfranco Zola seeks to bolster his attacking options.
West Ham would need to sell before they can buy but they could have as much as £5million available if James Collins completes a move to Aston Villa.