"We've had Carlton training with us for a while now and as soon as he's fit enough to play there will be an offer of a short term contract on the table there's no doubt about that," he told reporters ahead of the Hammers' Premier League game at Hull City on Saturday.
"That's why he's here with us and that's why we're trying to improve his fitness having missed pre-season.
"As soon as he's OK and suitable terms and conditions have been agreed, which is nothing do with me, then he'll join us for however long the contract is negotiated for."
Cole spent seven seasons at West Ham, scoring 59 goals in 237 games.
However the 29-year-old scored only twice in 29 appearances in 2012-13.
West Ham are in need of more firepower after record signing Andy Carroll suffered a foot injury on his return to training this month after injuring his heel at the end of last season.
The club, who have signed Croatia striker Mladen Petric on a one-year deal, have not set a likely date for Carroll's return.
Midfielder Joe Cole is still recovering from a hamstring injury but winger Stewart Downing is available again.
"Joe's not really injured anymore but we're just being protective of him and think he needs some more training before he's available again which I would have thought would be next week," said Allardyce.