Carroll has yet to play for the Hammers this term due to a heel injury after sealing a permanent transfer from Liverpool to Upton Park in the summer.
Allardyce has struggled to replace Carroll and was forced to go into the game against Tottenham Hotspur before the international break without a recognised striker.
West Ham managed to come away from White Hart Lane with a surprise 3-0 victory but they lacked an attacking threat in Saturday's 3-1 defeat by Manchester City as Ricardo Vaz Te's goal was one of only two shots on target.
A return date for Carroll has yet to be given but Allardyce understands he is making good progress and is waiting for further news this week.
"I will be speaking to the specialist on Monday to see whether he can give us at least a date when he thinks he will be able to come back to us," said Allardyce.
"He is still improving week by week and is probably due back with us I would hope. It is very important we get him back as quickly as we can as I don't want to be continuing to play with no front man."
Allardyce added: "Having got strikers who were not scoring was the only reason we played that system against Tottenham.
"Andy won't play in it. We bought him to be our leader of the front line. Once he gets fit and up and running, he will not only score goals but he will create opportunities for lots of other players to score goals."