The former England left-back has been promoted to manager David Moyes' senior coaching staff this season.
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Irvine told the Athletic: “Leighton is already a very good coach and could become a manager one day. He’s got good ideas about the game, and he’s very well prepared for sessions.
“He has a good way about him in terms of delivering it, real attention to detail, which is important.
“David would tell you, I actually forced him to sign Leighton (as a player). Joleon (Lescott) gave us an extra big one (at left-back), and he initially wasn’t sure about Leighton. I used to bang the drum for the small ones because I was a late developer.”