Allardyce insists Carlton Cole's form in the four-match winning run that has eased the Hammers' fears of relegation makes him a genuine contender to continue up front at Goodison.
Three of those victories were secured in Carroll's absence as the England marksman served a three-match ban for his red card against Swansea on February 1.
Carroll is available to face Everton, but Allardyce may opt for Cole after he was on target in Saturday's 3-1 victory over Southampton.
"Carlton has done a really good job while Andy has been out," Allardyce said. "It's a tough decision based upon how Carlton performed last week and obviously I'll make that decision on Friday when we pick the team to play Everton.
"After he spent a long time in the wilderness over the summer, it took a little bit of time to get him back into top condition and now he's done that he's produced more goals than he did last season.
"Goals are what it's all about for us at the moment. In our last four games we've won them all by two goals."
Carroll had only recently recovered from a long-term foot injury when he was dismissed against Swansea, a setback which contributed to him not being included in Roy Hodgson's England squad for the friendly with Denmark on March 5.
And Allardyce is backing the 25-year-old to prove he is worthy of selection.
"I don't see any reason why he can't make the World Cup squad," Allardyce said. "It's in his hands what happens between now and the end of the season based upon his performances, when selected.
"After a disrupted first half of the season last season he got into full flow and was selected by Roy Hodgson to go to Brazil.
"Unfortunately, because he was injured in the last game of the season against Reading, he couldn't make that trip.
"If he does the same again then there shouldn't be any problems with Andy being in that final squad for the World Cup.
"He's got to stay fit, perform well and that will give him a great chance of being selected."