Neville, 36, has retired as a player and made moves into coaching by taking up a role with England Under-21s at this summer's European Championships. There has been speculation linking him with a post at his first club Manchester United, under his old Everton boss David Moyes, but Martinez believes he could have a role at Goodison Park.
Martinez told evertontv: "I think Phil Neville is an Everton icon and I think he can bring a lot into his time as a coach. I really want to speak with him and see how he feels about his future."
Former England international Neville spent eight years with Everton after leaving United in 2005.
He said he would consider numerous offers to move into coaching full-time or step into the media after his involvement with England Under-21s ended.
Martinez is building his backroom staff following his appointment last week.
One man who will need replacing is former Scotland defender David Weir who, after being interviewed for the Toffees' top job, has left to become manager at Sheffield United.
Martinez said: "I spoke with David Weir and he is a phenomenal gentleman and it is a real shame - the timing of the opportunity of management is something he had to take.
"It is a real shame he hasn't been able to be part of the project because he is someone that would have fitted in really well."
- Sports & Recreation
- Phil Neville
- Manchester United
- David Moyes