The striker scored just the second goal of his season-long loan from Liverpool, which has been badly disrupted by injury, in Saturday's 1-0 win against Swansea.
Hammers co-owner David Sullivan confirmed on Friday that an agreement had already been reached with Liverpool to sign Carroll on a permanent basis, although they were yet to agree terms with the player.
But despite praising Carroll's ability, Allardyce admits he is uncertain whether the club will be able to secure the 24-year-old's signature permanently.
"You always want a top class centre forward," Allardyce told talkSPORT.
"I know he's been short on goals and he's had a disrupted season, but he'll only get better if he's got a settled future, whether that's with us or not [I don't know].
"It would be a long process though. We will have a conversation at the end of the season with Andy and Liverpool. It all depends on how he feels and what he does between now and the end of the season.
"It's also about where Andy thinks his future lies. He hasn't thought about that yet, he just wants to play as much as he can.
"There are not many of Andy Carroll's type. The sad thing for football is that it now seems unfashionable to have a big centre forward in your team, which really disappoints me.
"It excites people when you see him rise above everybody else to get the ball in the back of the net.
"I've known him since he was a youngster. I could see the talent that he had and that talent flourished very quickly into Liverpool paying £35million for him. It didn't work there for whatever reason but he's such a young man, who's desperate to play football and do well."