Neville, 36, could also be joined by Everton’s reserve-team coach David Weir, although both men may yet feature prominently in the search for Moyes’s successor at Goodison Park.
Weir, 42, also spent eight years as a player at Everton before returning a year ago.
Sir Alex Ferguson’s sudden retirement, and the appointment of Moyes, has created a degree of uncertainty among United’s coaches. Normally, if a manager is sacked or chooses to leave for another job, he is followed by his backroom staff, but this situation is different. There will not be wholesale changes, although it is understood that Moyes will be able to bring a couple of staff with him.
That leaves a question mark over Ferguson’s assistant Mike Phelan and first-team coach Rene Meulensteen. Phelan has considered management, having come close to taking over at Burnley in 2010. It remains to be seen if he and Meulensteen have a long-term future at the club.
Moyes wants to bring in someone he trusts, and Neville in particular could be a key figure in helping the new manager settle, considering his background with both clubs. A member of United’s famous 1995 Youth Cup-winning side, Neville lifted six titles as a player at Old Trafford and also won the Champions League.
Set to work with the England Under 21s at the European Championship in Israel this summer, Neville has maintained close ties with former team-mates like Ryan Giggs and Paul Scholes, who could also be given coaching roles by Moyes.