The Hammers' boss has confirmed that the Reds can exercise the option to bring the £35 million striker back to Anfield in the middle of the season if they wish to
Carroll made an impressive debut for the east London club against Fulham a fortnight ago, helping his side cruise to a 3-0 victory before suffering a hamstring injury in the second half of the game and Allardyce was quick to hail the former Newcastle striker's importance to the team.
"There's an opportunity for Liverpool [to get him back in January] if they want to, but whether they do or they don't will be in a matter of time." he told Sky Sports' program 'Goals on Sunday'.
|ALLARDYCE REACTION TO NORWICH DRAW
|9/4||West Ham are 9/4 with William Hill to score in both halves against Sunderland
The Hammers boss also revealed that Carroll wasn't the only big name striker he was after this summer, citing Dimitar Berbatov as another players who was on his radar.
He added: "We couldn't afford him [Berbatov]. The problem was the transfer fee and the size of the salary was out of our domain this season in terms of our budget.
"Fulham created their own transfer funds. They knew Clint Dempsey was moving on, and one or two others, and that gave them the opportunity to go big.
"They were interested in Andy Carroll as well, I believe, and we were glad to get Andy on a loan basis but they obviously clinched Dimitar Berbatov."