Carroll, who is spending the 2012-13 season at Upton Park, initially struggled for form under Sam Allardyce, but has since scored five goals and two assists in his last nine outings.
Cole, who also played with Carroll at Liverpool, has claimed that the 24-year-old is as good as another former team-mate of his, ex-Chelsea star Didier Drogba.
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|3/1||Andy Carroll is 3/1 with BetVictor to sign for West Ham this summer
"You can see him in the tunnel and he intimidates centre halves with his long hair and broad shoulders, throwing them about. He's been a real handful.
"It's great to see him playing with so much confidence and with a smile on his face."
Goal.com exclusvely revealed on April 28 that Carroll is intent on proving his worth at parent club Liverpool, despite West Ham co-owner David Sullivan opening talks with the Reds over a £10 million summer switch.
Cole understands Carroll's predicament, but confirmed that West Ham are very keen on extending the striker's stay at the club.
"West Ham definitely want to keep Andy Carroll," he added.
"I don't know the ins and outs of the deal but the way he's been playing in the last couple of weeks you can understand why Liverpool paid £35 million for him a couple of years ago.
"West Ham would like to keep him; he's our top scorer. He's got to do what's right for him though."