Allardyce said he may take a "calculated risk" and include the striker in his squad who are 19th in the 20-team table, without a win in their last seven league games and have conceded 11 goals without reply in the last week.
"Andy's been training okay. We've got to talk to the lads who are looking after him and see if he's ready," Allardyce told a news conference on Friday.
"We're going to see how training goes today and then make a decision from there."
The West Ham boss is under pressure following successive humiliating defeats in the last which saw them beaten 5-0 at Nottingham Forest in the FA Cup and 6-0 at Manchester City in the Capital One (League) Cup, and admits that circumstances may force his hand with Carroll.
"Ideally we'd like to progress it a little slower but based on the circumstances, in terms of where we are, then it may be a calculated risk which I'm prepared to take," he said.
Carroll is not the only player out injured with Allardyce also hoping that either of his defenders, James Tomkins or James Collins will also be fit.
Allardyce also confirmed his interest in Inter Milan striker Ishak Befodil and explained that he had hoped to announce the signing of an unnamed player, but those plans had hit a snag.
"We're trying, we've been trying for several weeks (to sign Befodil).
"Certainly I thought I would be talking about one player today that we would have had in the country and signed or nearly signed but that fell into some paperwork problems yesterday."
There was widespread speculation on Friday that West Ham are considering offering the manager's job to Billy Davies, manager of the Forest side that beat West Ham last week, but that supposes they are losing patience with Allardyce.
The board gave Allardyce their full support in an open letter to fans on Tuesday, but with only one win in their last 10 games in all competitions, that patience might not last much longer.
(Reporting by Sam Holden, editing by Mike Collett)
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