The Hammers manager made a successful bid to take the England international on a season-long loan at Upton Park in July, with a view to a permanent transfer reported to be worth £17m at the end of the campaign.
However, Carroll, who cost Liverpool £35m in January 2011, was unwilling to move to east London,
But Allardyce maintained he would be happy to take the former Newcastle forward on loan if the move became a possibility.
“Many things in the final week of the transfer window emerge and should it be the case that we would be able to do something then I think it would probably only be a loan,” Allardyce said.
“We would see if we could pursue it and clinch it, but if we only finish with Matt and nobody else I would be happy with the squad I’ve got.
“While it is not quite as big as I’d like it to be, I think it has got a lot of quality.
“My problem is there may not be funds available for Andy now.
“If Andy became available or anybody became available and they wanted to join West Ham, I would ask the owners.
“At the moment that is not the case and we just have to wait and see if and when that situation arises.”
Carroll, who worked with Allardyce at the Magpies in 2008, has scored 11 goals in 57 appearances for the Reds since moving to Anfield.
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