Cole spoke of his interest in the role last month but this week revealed he was given a 'polite no'.
He said, "I sent in my CV. It's the only job I have ever applied for.
“I got a polite no. But I would have loved the opportunity to stand in front of them and be interviewed.
“Managing the Under-21s is the only job I would step away from what I am doing now for. The job is so unique."
He added: "I would have loved the job but it was politely declined.
"No grudges and I hope whoever gets the job is someone of my ilk, an ex-player who has experienced all of that."