Carroll moved to Liverpool for £35 million as a replacement for Fernando Torres but the move never quite worked out, leading to a season-long loan at West Ham in the summer. The east Londoners have the option to make the deal permanent for an undisclosed fee, although reports this week suggest they will reduce their offer.
Asked whether he would stay if West Ham put the right money on the table, Carroll said: "We will have to wait and see. It is obviously a great club and I do not see why not."
Carroll has also been linked with a move to former club Newcastle and the striker is not sure what the future holds past the end of the season.
"I have just got to wait and see, really," he said. "We'll see what happens at the end of the season. Obviously I don't know what is happening so we will just have to wait and see.
"It has been great here and every minute has been fantastic. The lads have been great, the gaffer has been great and the fans are unbelievable."
Carroll netted his sixth West Ham goal on Saturday to earn a hard-fought point at Southampton. The England international saw his driven strike deflect in off Steven Davis, levelling just seven minutes after Gaston Ramirez had given Saints the lead.
"It was a bit windy," he said. "The ball was all over the place but we came here and got a result. In the first half I was getting blocked off and there was a few players around me. I was talking to the referee a bit but it was a difficult day to me.
"With my goal, I just had to hit the target. Obviously it got a little bit of a deflection and went in, which sometimes happens. I have had a few injuries over the years and I am just getting over them now so it is good to get on a run of games and goals.
"I had a few chances and I think we could have won the game in the end. We are disappointed not to but happy we got the point."
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