Cole wants to see "more desire and passion" from Martial after the striker recorded his first 20 goal season at United.
"We all get caught up in the debate about Martial," he told the Athletic.
“I'm not sure where he wants to play. He's played well this season as a centre-forward and has scored more goals this season than any other but he should have scored more than 20 in more than one season.
"He came for big money and he's very talented. He has to show more desire and passion at times. He's got good feet and a lovely first touch.
"He's got blistering pace too but you don't see it enough. He wants the ball to his feet but he should mix it up a bit more."