Despite the striker currently being on loan on a season-long deal from Liverpool and a fee agreed with his parent club, the Hammers boss is still undecided on the striker's future
The 24-year-old joined the London side on a season-long deal from Anfield in August, but has struggled for form after a number of injuries, leading to just two goals in 12 outings.
Carroll joined Liverpool in January 2011 for a British-record fee of £35 million, before being shipped out on loan, and Allardyce feels more stability for the striker would benefit his on-field displays.
"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."
Allardyce feels Carroll holds a unique set of attributes among today’s modern footballers, and feels Liverpool may not be the best home for him as he continues his progression.
He added: "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."