Carroll 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 former Liverpool forward to earn a place in England's FIFA World Cup squad, Carroll is not guaranteed to start at Goodison Park given Cole's impressive recent displays.
"It's a tough decision over Andy based on Carlton's performance last week, so I'll make that decision tomorrow," said Allardyce at a press conference on Thursday.
"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 games, and Allardyce expects another tough challenge.
"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."
