Carroll has been out with a knee injury since November and has missed six games.
But he is due to start running tomorrow and Allardyce has no intention of cancelling Carroll’s loan.
He said: “I hope it will be no more than three weeks before Andy is playing again. He’s not in full training yet but he’s due to start running this week.
“The trouble is that because he’s such a big lad he’s a bit more delicate when he’s coming back from a knee ligament injury and we want to make sure he is properly fit and stays that way when he comes back.
“He’s missed a huge chunk of games with the two injuries he’s had since he joined us.
“Andy has only got one goal for us so far and he has to score more. All of our forwards have got to get better at finishing.
“The only disappointing thing about our win against Norwich was the number of chances fluffed.”