The Spaniard now looks odds-on favourite to succeed Moyes at Goodison Park.
Wigan Athletic manager Roberto Martinez has confirmed that he will be leaving the Latics this summer after talks with chairman Dave Whelan, adding to speculation that he is to become the new Everton boss.
Martinez and Whelan had discussions about his future last week, following the relegation of Wigan and the Spaniard’s constant links with the vacant managerial positions at both Everton and Stoke City.
“He wanted permission to move so I’ve given that,” Whelan told BBC Sport.
“He feels he’s not the man to lead us back into the Premier League. I’ve got to accept what he feels.
“He loves Wigan and the fans. We have to move on now and want applications for the job.
“If he decided to leave us, he is a must for Everton. He plays football from back to front, and Everton like to play football from back to front. In my mind he is tailor-made to manage Everton.”
The 39-year-old took over at the DW Stadium in 2009 following a successful spell at Swansea City and steered the Lancashire side away from relegation, against the odds, in both 2011 and 2012.
However, Wigan and Martinez’s luck ran out at the end of this current campaign as a 4-1 defeat to Arsenal confirmed their demotion to the Championship with one game to spare.
The relegation marked a few days of mixed emotions in early May, as just three days before the Gunners loss the Latics had shocked most people by beating Manchester City 0-1 in the FA Cup final – lifting the trophy for the first time in their history.
Ever since the news that David Moyes would be leaving Goodison Park to take over from the retiring Sir Alex Ferguson at Manchester United, Martinez has been strongly linked with the Everton job.
Now it seems that the talented young manager will be heading to the Toffees with Mark Hughes seemingly in the process of being installed as the new boss at Stoke.
Wigan will now be on the hunt for a new man who can bring back Premier League football at the first time of asking.