The Spaniard is being linked with a Latics departure following the clubs relegation from the Premier League and the Toffees are keen to bring him to Goodison Park to replace David Moyes who has moved into the Manchester United hot seat.
Wigan chairman Dave Whelan has revealed that Martinez wants to leave the club he led to FA Cup glory last season and has made it clear that he would depart with his blessing.
"Roberto wants to move on and I have got to accept it," said Whelan.
"Everton rang me and I said they have permission to talk to him. I would never stop Roberto talking to football clubs.
"We will let him go but he's on a 12-month rolling contract so if he moves someone will have to buy him out of his final year.
"We are still friends, we will always be good friends and he will always be a friend of Wigan Athletic."
He added: "He does not feel he is up to the task of getting us back into the Premier League.
"Football is football and I understand where he is coming from.
"Everton are a nice club and have a great chairman in Bill (Kenwright) and he is an honest man."