The Gunners hitman has been out of favour at the Emirates and looks set for a loan deal away from the north London club in the January transfer window.
And, speaking to the Alan Brazil Sports Breakfast show, the Hammers chief insists he does want the former Bordeaux man – but only if it makes financial sense.
“We’re still looking [for new players], We have made an enquiry (for Chamakh),” he said. “If there’s a deal to be done then we’ll have a look at it.
“I cast my mind back to what Chamakh did with Bordeaux where he won the Ligue 1 title and helped them into the Champions League.
“He produced some wonderful goals and performances, there’s something in there but whether we can do something financially I don’t know.”
He added: "The situation I have with [Andy] Carroll being injured and [Modibo] Maiga away at the African Cup of Nations means I only have Carlton Cole available."