Carroll has endured a difficult time in east London since he arrived on loan from Liverpool last summer but he looked back to his menacing best, scoring a fine brace which eased any lingering fears of relegation for Allardyce's men.
The 24-year-old fired a bullet header past Ben Foster to put West Ham 1-0 up and he then sealed the victory with one of the goals of the season following Gary O'Neil's strike.
Carroll watched the ball come over his shoulder after James Collins had sent a long punt up field and he volleyed past Foster with his right foot from a tight angle.
When asked whether he would like to retain the 6ft 3in striker's services next season, Allardyce 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."
Carroll's time in London has been blighted by injury but he is now fully fit and judging by this performance, it will only be a matter of time before he earns an international recall.
Roy Hodgson omitted Carroll from his squad for the double-header against San Marino and Montenegro but when the England manager comes to watch the footage of this game at Upton Park, he will be impressed, Allardyce reckons.
"That was the best we have seen of him here," Allardyce added. "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."
- Sports & Recreation