Cole is set to lead West Ham's line when they travel to West Bromwich Albion tomorrow.
Hammers manager Allardyce said: "Carlton has contributed well.
"He has not played quite as much as he'd wanted to but, when he has got the chance, he's done the business.
"We now need him to continue that. With Andy out for a number of weeks, Carlton can establish himself in the team and keep his place. It'll be Andy's problem to get back in.
"In fact if Carlton's playing that well when Andy gets back, it's nearly impossible for me to leave him out."