The 24-year-old scored twice in West Ham's win over West Brom on Saturday but is only on loan from Liverpool and is due to return to Anfield in the summer.
However, he appears to have no future on Merseyside under Reds boss Brendan Rodgers and Allardyce says he would be keen to sort out a permanent switch for the England international at Upton Park.
Allardyce said: "There is always a possibility. We will look at the end of the season and we will see what negotiations can be done."
Carroll joined Liverpool for a club-record £35m fee in January 2011 but struggled with injury and form in his first year at the club and was loaned out when Rodgers arrived in the summer.
His double against the Baggies means he has scored five for the London club and Allardyce hopes he can enjoy a good end to the season.
He added: "That was the best we have seen of him here, because he has put two goals in, on top of a good performance.
"I hope this kicks him on to being a regular scorer for us in the next eight games.
"He is in a good frame of mind now and, finally after a long wait, his fitness is good and that's why you are seeing these performances and the goals are coming."