He also went on to state that he thinks the forward's heel injury will keep the England man sidelined up to mid-November.
Carroll has yet to feature for the Hammers this season after suffering a problem with his foot which has required treatment from some of the top medical professionals in both Europe and the USA.
Reports had suggested the 24-year-old club-record signing could be back training with his West Ham team-mates following Sunday's Barclays Premier League trip to Swansea but Allardyce was quick to quash such rumours.
"The stories that Andy Carroll is returning to us this week are not true," he said.
"There is still a while to go there. He'll be back we hope in the next two to three weeks. Hopefully he can start full training when he does come back. It's always been a week-by-week assessment.
"He is frustrated of course and is desperate to be playing football again, it's what he loves doing most. I will only be too pleased to get him back in the squad."
West Ham's other forwards have struggled for goals in Carroll's absence and Allardyce has played the last two league matches without a recognised striker as a result.
The two games provided differing outcomes, a 3-0 win at Tottenham was followed by a 3-1 home reverse to Manchester City, and Allardyce is still to decide whether to play without a striker once more and the option of using a fit-again
Carlton Cole from the bench would be something to consider.
"It's worked very well in the first game, not so well in second," he said.
"It will be our choice in the next few days about whether we change the system.
"Carlton Cole played another under -21 game last Monday. Our under-21s are top of the league, that's great news from the younger end.
"I don't think Cole is ready to start from a match fitness point of view but his experience from the bench is invaluable at the moment."
West Ham currently sit 15th in the table and have taken eight points from eight games so far this season, a record which Allardyce hoped would be better at this stage, with results at Upton Park a particular concern.
"I couldn't knock the performances too much but I think we're about four points short of what we should have achieved," he added.
"My huge concern is the fact that we've lost three home games on the trot, that never happened last season and if fact we only lost four all season at home.
"That's my biggest worry, our away performances have been very good but our results haven't matched the performances. We should have beaten Newcastle, we certainly shouldn't have lost against Hull City we had a good draw at Southampton and a great win against Tottenham.
"We've got to make sure we give our all in the Premier League because we're a 100 per cent team and we need to play at 100 per cent to win a game of football in the Premier League."
The Hammers lost 3-0 at Swansea in their first away fixture of last season, with Wales defender James Collins gifting the crucial second goal of the match to Michu.
The 30-year-old will not get the chance to make up for his poor display at the Liberty Stadium this time around as he remains sidelined with a hamstring problem.
Along with Carroll and Collins, only Alou Diarra is absent and Allardyce also confirmed Jack Collison would return to the club on Monday after completing a short loan spell at Bournemouth