Neville, who made almost 400 appearances for United before joining Everton in 2005, is expected to replace Rene Meulensteen as first-team coach. The 36-year-old, Moyes's captain at Everton, had expressed interest in taking over as manager at Goodison Park.
With Meulensteen understood to have turned down a different role, four of Sir Alex Ferguson's senior backroom team will have departed the club. The assistant manager, Mike Phelan, Eric Steele, the goalkeeping coach, and Martin Ferguson, Sir Alex's brother, the chief scout, have all left.
Round, who has been Moyes's assistant manager at Everton since 2008, should take Phelan's position. Woods is in line to take over from Steele and Cooke, the chief scout at Everton, is likely to replace Ferguson.
It is unclear if Moyes, who hopes to persuade Wayne Rooney he has a future at United, has been able to speak with the striker. The birth of Rooney's second son and the fact that the forward was joining up with the England squad on Sunday, plus Moyes's plan to take a holiday this week, means time for them to meet has been limited.
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