The England international joined Liverpool in January 2011 for a fee of £35 million from Newcastle but, after a tough 18 months, he moved to the Hammers on a temporary basis.
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The 24-year-old told Sky Sports: "I've loved every minute the lads have been great. There are still a few games left [but] I've got to wait and see what happens."
Allardyce added: "The implications of Financial Fair Play will take its toll, and that might be a case where it takes its toll.
"I'm not absolutely certain yet [whether we can afford Carroll] because our budgets haven't been set yet, but it can be a deciding factor in terms of where we go and what we want to bring in next year.
"It makes our lives a little bit more difficult, but I can understand everybody wants a bit more financial stability. I can understand that but it doesn't make my life any easier."
Both were talking after the 2-2 draw at home to Manchester United on Wednesday night, and Carroll relished the physical battle against Rio Ferdinand and, in particular, Nemanja Vidic.
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"It was a great tough battle I enjoyed getting stuck in giving and getting a few elbows."
Carroll almost got himself into trouble with the referee after a minor with Wayne Rooney but the former Newcastle man dismissed that as "banter" before claiming that a heavy collision with David de Gea moments later was not intentional.
"It was a bit of friendly banter with me and Wazza," he explained. "I just went for the ball that's all it was. I was running straight in to get the ball and couldn't stop when I was flying through the air."
The Hammers took the lead twice in the match but Carroll admitted that their poor ball retention played into United's hands, noting: "They came out and passed it well. We were sloppy giving it away for their goal."