Carroll looked back to his menacing best, scoring a fine brace which eased any lingering fears of relegation for Allardyce's men.
When asked whether he would like to retain the 6ft 3in striker's services next season, the West Ham manager said: "The answer to that would be yes.
"There is always a possibility. We will look at the end of the season and we will se what negotiations can be done.
"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."