The 24-year-old is likely to leave Liverpool after reportedly being told that he does not feature in Brendan Rodgers's plans.
The Hammers have a £17m option to buy the England international, with some reports suggesting that they will consider trying to renegotiate a lower price.
Allardyce said that Carroll has huge potential and has still not hit the peak of his powers.
"The next move is a critical one for him," The Mirror quotes Allardyce as saying. "It's about playing, improving and scoring goals. That next move has to implement all of that for the team he plays for and him.
"He is still developing and is not in his prime. He is still two or so years from his prime.
"Considering what he can grow into with those talents - and something nobody has got which is size; physical presence, with talent - if you marry those together, his threat is a very big talent indeed, and a very difficult one to stop."
Carroll has scored six goals in 19 appearances for West Ham this season.