Inter Milan have confirmed their interest in Cardiff's Gary Medel but have given up on Man City forward Stevan Jovetic.
Jeffrey Schlupp and Liam Moore have signed new deals with Premier League newcomers Leicester City.
The 36-year-old called time on his playing career at the end of last season following an eight-year spell at Goodison Park.
He has since been involved in coaching the England U21s side that was knocked out of the European Championships in Israel at the group stage.
Neville must now decide where his future in the game lies and Martinez is convinced he would make a good coach.
"I think Phil Neville is an Everton icon and I think he can bring a lot into his time as a coach," Martinez told evertontv.
"I really want to speak with him and see how he feels about his future."
Neville made his name at Manchester United before joining Everton in 2005 and was named skipper by David Moyes in 2007.
He has sat his coaching badges over the last few seasons but admits he has a big decision to make.
"I have got two paths - one to go into the media, the other to go into coaching and management," Neville said last week.
"I have got offers from both. I will sit down at the end of the tournament."