The Toffees announced earlier this month that Martinez had been sacked following a 3-0 away defeat to Sunderland, which summed up a disappointing season for Everton.
Martinez, who guided Everton to fifth place in his first season in charge, oversaw a bottom half finish for the second season in a row this term, and given the players at his disposal, they should have been performing a lot better.
Now, with the season over, the search for a new manager begins at Goodison Park, with a host of big names already touted for the job.
Now, pundit Tony Cascarino has been speaking about the situation, and has told The Irish Sun that he thinks Stoke City boss Mark Hughes should be a top candidate.
The Welshman guided the Potters to a ninth placed finish this season, and has certainly rebuilt his reputation at the Britannia Stadium after a difficult spell in charge of Queens Park Rangers.
The 52-year-old has been heavily linked with the Everton job, having spent a short time with Everton as a player, scoring one goal in 18 appearances for the Toffees.
Cascarino believes that Hughes should be a frontrunner for the Everton job as his managerial record is 'fantastic', and praised him for building on Tony Pulis' success at Stoke by mixing in talented players like Xherdan Shaqiri, Marko Arnautovic, Bojan and Ibrahim Afellay.
"Stoke boss Hughes has a good shot at it as a former Everton player who was popular with the fans when he was there in 2000," said Cascarino. "His managerial record is also fantastic. He’s managed to keep up the fine work done by Tony Pulis at the Britannia, while also changing their style of play, and that’s earned him a lot of plaudits. Rightly so."
"Critics will point out how his QPR stint was poor. But you just have to look at how everyone at Loftus Road has struggled in recent years. It’s a difficult club to manage. Also, show me any manager who has a CV as lengthy as Hughes’ — Wales, Blackburn Rovers, Manchester City, Fulham, QPR and Stoke — that has no blemishes. Bar the Rs, he left every other job with his head held high having done a fine job," he added.
Would you like to see Hughes replace Martinez at Everton?