Cole had been working as Carsley's assistant with the U21s before taking the Cremonese job last week.
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Carsley said of the Chelsea great: "He's desperate to have his own team and to really have a go at doing it.
"I've probably seen a little bit of frustration at times of from him, not getting the opportunities that he probably can see other people getting.
"It's brilliant that he's got the chance to manage. I speak to him most days, and he's so excited and enthusiastic about the opportunity.
"He’s had some good jobs but to get that chance as a head coach, he’s probably had to wait that little bit longer. He's done the (hard) yards. He’s really committed to being a manager."