Carroll has a troublesome heel problem and there is no date yet for when he might resume full training.
Allardyce said: "When Andy gets back training it's probably the best part of four weeks before he gets back onto the field in the first team. He has to start a four-week pre-season. We'd try to speed that up if we possibly could."
Allardyce believes the lack of goals are not down to the strikers alone.
He said: "The problem is our goals were shared out last year. All the players in our team scored. Kevin (Nolan) got 10, Andy (Carroll) got eight, everybody else got three two or one and that's why we finished 10th.
"None of those players are scoring goals as they did last year. It's not just the front end, it's all the players not scoring.
"When we get that right, which I think we will, we'll start getting three points instead of one."
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