Appleton, 48, began his professional career after graduating from the United academy and went on to play for the club for five successful years from 1992 to 1997. After his time at United, he made a permanent transfer to Preston North End.
He entered football management in 2011 and was most recently in charge of League One side Charlton Athletic before the Addicks sacked him in January.
Appleton has also previously managed Blackpool, Lincoln City, Oxford United, Blackburn Rovers and Portsmouth.
The ex-midfielder is currently out of work, but according to the Daily Mail, he recently had to opportunity to become United’s loans manager.
That job would’ve seen Appleton oversee United’s young players who have been sent out on loan to other clubs.
Appleton, though, has turned down his old club’s offer, and United must now find someone else to fill the role.
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Up NextNews of Appleton snubbing United comes after two other former players – Ruud van Nistelrooy and Rene Hake – returned to the club in coaching roles.
Van Nistelrooy has put his own managerial career on pause to work under Erik ten Hag and is desperate to help the Red Devils get back to the their best.
‘It’s 100% the right decision [to return],’ Van Nistelrooy told TNT Sports. ‘I felt a strong feeling that I want to help build United – little by little – back to where we feel and know where the club should be.
‘I was on the managerial track. I managed PSV – an unbelievable experience – and I was in talks with clubs to manage, and I love it. I had my staff all ready, and then I had a phone call. I was like, ‘jeez’. I never thought of it as a possibility.
‘Erik called me. I said I had to think about it, but I immediately felt, ‘wow’. I started to love the idea. Especially the big picture where it’s a new start with the new ownership and leadership. A phase where you start to rebuild and be a part of it.
‘I just want to contribute to where the club should be and, little by little, bring it there. I hope when they reach it, it will be soon. I want to contribute. I feel a strong feeling that I want to do that.’