Darren Moore has been widely tipped to retain the West Bromwich Albion job permanently.
Joleon Lescott and Kevin Kilbane both played under David Moyes at West Ham.
Wolverhampton Wanderers won in the Championship on Wednesday.
Everton are said to be closing on the signing of Man City defender Eliaquim Mangala.
The Fulham star could follow a long line of Moyes success stories from the Football League.
Wolverhampton Wanderers have been magnificent so far this season.
Sean Dyche is one of the front runners to replace Ronald Koeman at Everton.
Tottenham Hotspur lacked any real kind of cutting edge against Manchester United on Saturday.
Oumar Niasse was Everton's hero against Bournemouth last weekend.
Former England defender Joleon Lescott was asked whether he would prefer to join Tottenham Hotspur or Arsenal if given the choice right now.