Having been sidelined with successive heel injuries which have ruled him out since the final day of last season, the 24-year-old is yet to feature for the Hammers since making his switch from Liverpool permanent over the summer.
Carroll also saw his comeback halted by a recent stomach infection and Allardyce says that he is still in the dark about when the England international will be available for selection again.
"We've been trying to get a date out of the guys over in Amsterdam," he told Sky Sports News.
"But they're reluctant to give us any clear indication of just how long it's going to be before he can join us back here and start training with the players, with the squad and then obviously getting into the team to play some games.
"It's obviously a great worry and concern for us all and one we haven't expected, but one we have to make sure we deal with."
Allardyce has often opted to play without a recognised striker so far this season, but admits that he did attempt to bolster his attacking options during the summer.
"We tried to sign four top strikers before the window shut in August, so we didn't just sit back and not try to sign the one player we felt would add to the situation," he said.
"As I said, we tried our very, very best. David Sullivan and David Gold tried their very best to sign a top, top striker.
"Unfortunately, none of the players that we went for wanted to join West Ham at the time."