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.
"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."
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