Eyebrows were raised when United made Martial the most expensive teenager in football history last summer but the 19-year-old has proved a bright spot in an otherwise disappointing campaign for Louis van Gaal's side.
Cole, who won five Premier League titles under Sir Alex Ferguson, compared Martial's ability to stretch defences with his speed to Leicester City star Jamie Vardy.
“Anthony has been very good since he arrived,” Cole told United Review. “For such a young man with such a big fee on his head, the way he’s gone about his business has been really, really impressive.
“He’s had a lot to contend with, with the way this season has gone, but he’s slotted in very well, which is testament to him.
“He is the silver lining so far this season. He came for a lot of money and was an unknown, whichever way you look at it, but the way he’s adapted to the Premier League is brilliant.
“What I like about him is that he’s always prepared to have a go at people. What we don’t see a lot of now, and Jamie Vardy has done this extremely well for Leicester, is strikers who run in behind and stretch defences.
“You don’t see that a lot in the Premier League any more, but when Martial plays centrally he can do that. And when he gets in the box, he knows how to finish.
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"When he plays on the left also, he’s prepared to pick the ball up, run at people and go in behind people. That’s a massive asset in today’s football.”
Cole sees similarities between Martial and Arsenal and France great Thierry Henry in the way the 20-year-old has featured on the left flank as well as at centre forward.
“His understanding of the game is very good for a young man,” Cole continued. “If you asked Anthony where he wants to play then I think he’d say centre forward.
“I remember playing against Thierry Henry when he was at Monaco. He was on the wing and you’d just say to yourself, ‘that’s not his position,’ but then when he came to Arsenal he was used as a centre-forward or coming off the left, and he just did his thing.
“That’s going to be Martial, definitely.
“He’s got the temperament to do just that. He doesn’t strike me as a kid who’s into the high life. He’s a young man who wants to be the best he can be.
“However, you look at the game now, there are kids in his position who think they’ve already cracked it, but this boy can go all the way to the top, for sure. He’ll have a massive future in the game if he keeps developing.”