The 29-year-old, who saw his previous contract at Upton Park expire at the end of last season, has spent time training with the Hammers.
Allardyce has expressed a desire to bring the England international back on board, as he remains light in the striking department.
Attempts to bring the likes of Romelu Lukaku and Nicklas Bendtner into the club failed on transfer deadline day, meaning free agents are now the only available option.
Cole is, however, not yet fit enough to join the West Ham ranks and will not be offered terms until he is ready to compete for a starting berth.
Allardyce said in the Daily Star: "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.
"We still have one place available in our squad, with 24 players currently named, so we still have one place left for somebody.
"We have George McCartney back training with us, Joe Cole and Stewart Downing are very close to re-joining the team and after the Everton match they will probably be back in full training.
"If Carlton proves that he can be the player we all know he's capable of being, then hopefully he'll join us as well."