The Hammers' manager has told the 29-year-old striker he will keep the injured Andy Carroll out of the side if he maintains his fine performances for the high-flying London side
The 29-year-old was instrumental in the Hammers' 3-1 home victory over Chelsea on 1 December, and played well again as his side narrowly lost to Liverpool 3-2 on Monday.
And although 23-year-old Liverpool loan signing Carroll is Allardyce's first-choice striker at Upton Park when fit, the manager has told Cole the place in the team is his if he can keep his performance levels high.
"[Carroll's] out for a number of weeks so [Cole] can establish himself in the team and can keep his place if he wants. It will be Andy's problem to get back in," Allardyce told reporters.
He continued: "They were two fantastic performances against Liverpool and Chelsea. He's contributed well. He's not played quite as much as he wanted to but when he has got the opportunity he's done the business.
"Let's hope Carlton can continue to play that well and when Andy gets back it's nearly impossible for me to leave him out."
The Hammers' manager also had praise for Carroll, and suggested the forward still has plenty of time to develop his game and become an even better player.
"With Andy he's a brilliant player, I knew he was a brilliant player before he came here.
"He just needs the right break and once he gets going - I know he's only 23 at the moment, but the funny thing about the striker role, or the one we play, is that it takes a long time to learn," he added.
"For Andy to have that skill so young is a real blessing for him because I had to mould myself into that player.
"You'll see the best of Andy Carroll when he's 29 or 30, but right now he's still learning his trade."
West Ham face West Brom on Sunday afternoon, and can climb to seventh place from 11th with a win at the Hawthorns.