The Hammers released the ex-Chelsea youth player at the end of last season after failing to agree a new deal with him.
However, after being unable to land a number of attacking targets over the summer, ‘Big Sam’ is believed to be keen to re-sign the 29-year-old.
A move was thought to be close to completion a matter of weeks ago, but it collapsed due to concerns over Cole’s condition.
Since then he has been training with the Londoners’ first-team in a bid to prove his fitness.
Allardyce says that once the club are convinced that the forward is ready for action contract talks will re-open.
“He’s training with us at the moment and hopefully when Carlton gets fit enough to be part of the squad then we’ll talk to him about the contract situation,” he told the Daily Star.
“We still have one place available in our squad, with 24 players currently named, so we still have one place left for somebody.
“If Carlton proves that he can be the player we all know he’s capable of being then hopefully he’ll join us.”
Cole was linked with a summer move to French side Saint-Etienne, but the proposed deal collapsed due to a wage dispute.
Does Carlton Cole deserve another chance at West Ham?
Get involved below!
[cat_link cat=”west-ham” type=”grid”]