The London club parted with £15million to make Carroll their permanent property in June. The hulking striker had impressed during a loan spell at Upton Park in 2012-13, and the deal relieved £10.75m Matt Jarvis of his status as West Ham's record signing.
However, the England international has yet to feature this season due to a heel injury and Allardyce's men have struggled for goals in his absence.
West Ham played out a second successive 0-0 draw at home to Aston Villa on Saturday and have failed to score in six of their 10 Premier League outings, but Allardyce has played down talk of Carroll returning in the near future.
"(When) Andy Carroll gets back to full training, it's probably the best part of another four weeks before he gets back on the field in the first team, because he has to start a four-week pre-season, which is the minimum time for a pre-season," explained the West Ham manager.
Allardyce also revealed that Carlton Cole, who recently ended a five-month spell without a club by rejoining West Ham and made substitute appearances against Swansea City and Villa, has insufficient match fitness to make his starting XI.
"We have to use him sparingly, because he's in the middle of a pre-season so he can catch up with the rest of the lads," said Allardyce.
