Carroll has scored six times during a season-long loan in east London, with the Hammers' boss lavishing praise on the 24-year-old for his recent form.
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"I thought Andy was very, very good," Allardyce told reporters after his side’s 2-0 win against Wigan on Saturday. "Some of his movement was excellent. If he keeps on showing such good form then I believe it improves our chances of signing him.
"He is critical to us moving forward as a club and to our development programme. If we haven't got him next season, we'll have to make a big-money signing in his place."
With West Ham now on 42 points and virtually sure of another season in the Premier League, Allardyce confirmed he will be signing a new contract when his side’s safety is guaranteed.
He said: "The contract is sorted and I will sign it when we are mathematically certain [of staying up]."