Everton boss David Unsworth has been placed in temporary charge since Ronald Koeman was dismissed.
Everton take on Lyon and Watford in the coming seven days, before the international break.
And Neville is expecting the Toffees to put a new man in charge over the two week break from club football.
At the moment Everton have David Unsworth in charge, and Neville feels that the temporary boss has done enough to show he should be given the role on a full-time basis.
He said: “Everton have two more games – away against Lyon in the Europa League on Thursday and then at home against Watford on Sunday – before the international break.
“Then they will have 10 days without a game, which is when I would expect a permanent appointment to be made.
“The only one of those four games to be at home is against the Hornets, and that is the one that is probably a must-win for “Unsworth individually, when it comes to his own future.
This is a great opportunity for him and I already think he has made a difference to this Everton side, despite losing both his games so far.”
Unsworth has been in charge of Everton since Ronald Koeman was fired, but he has been unable to find the winning formula.
Everton have been beaten by Chelsea in the League cup and, most recently, Leicester in the Premier League since Unsworth took charge.
The Merseyside outfit now appear to be fighting a relegation battle, and sit in 18th place in the Premier League table.
At the moment Unsworth still remains the bookies’ favourite to land the Everton job permanently.
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