The former Newcastle frontman and club-record signing is available again for Saturday's trip to Everton, having served a three-game suspension following his sending-off against Swansea City.
However, even though Allardyce has backed the 25-year-old to earn a place in England's World Cup squad, Carroll is not guaranteed to start at Goodison Park given Cole's impressive recent displays.
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|10/1||Carlton Cole is 10/1 with bet365 to open the scoring against Everton|
"Now Carlton is back in top condition he's produced more goals than he did last season. Our goalscoring has been good recently.
"We'll need all the confidence and ability we've shown recently to get a result at Everton."
Referring to Carroll's England hopes, Allardyce added: "If Andy ends the season as well as he did last year there shouldn't be any problems about him being in the final squad for Brazil."
West Ham have not won at Goodison Park since 2005, a run of six fruitless away trips, and Allardyce expects another tough challenge this weekend.
"We know it's going to be a tough, tough match for us, even if they have lost three out of their last four," he added.
"Roberto (Martinez) has carried on where David Moyes has left off and now it's about what they can do in the final push."