Montpellier coach Jean Fernandez has resigned after overseeing a run of seven Ligue 1 games without victory.
Liverpool goalkeeper Pepe Reina would welcome a return to Barcelona next summer.
Everton are confident they will have no difficulty in attracting a top-class replacement for David Moyes after he was appointed Sir Alex Ferguson's successor at Manchester United.
Chairman Bill Kenwright said it was vitally important they recruited someone "equally significant" to their departing boss, who remains in charge for the Toffees' last two matches before officially taking over at Old Trafford on July 1.
Already former Wales manager Mark Hughes, soon-to-be-leaving Everton captain Phil Neville and newly-promoted Cardiff boss Malky Mackay appear outside bets.
Hughes' stock has fallen after he was sacked by QPR in November, Neville wants to extend his playing career and has no managerial experience while Mackay is untested at Premier League level.
And, while the club expect to move quickly, it's understood the feeling within Goodison Park is there is no need to rush the appointment as the Everton vacancy will be regarded as one of the best in Europe with very few of the continent's 'serious' clubs having positions available.
"We've had a good 11-year adventure with David and it is my job and the club's job to get a worthy successor and build on what David has brought to the club and hopefully move on from there," said Kenwright.
"We will be out there finding the right man for this football club.
"It is important Everton continues in the David Moyes tradition, in the Everton Football Club tradition, with an equally significant manager - because he has been a significant manager for 11 years.
"Eleven years ago I made a decision and it was an instant decision when I met David, but I don't think that can happen this time.
"We have to be very seriously looking to see what kind of candidate is out there who can take the club forward."
Everton look set to finish in the top six again this season and expect the challenge of taking them to the next level, combined with a more secure financial footing than they have had for the last three years, will attract the best talent.
The club will receive an extra £20million from next season's new television deal and, although a portion of that will have to be used to pay off some of the £48million debt, it means there will be no requirement on the new manager to sell players.
It remains to be seen what agreement - if any - has been made with Moyes in relation to him returning to buy some of his former players, but even if he does Everton are confident they will not be sold short.
Midfielder Marouane Fellaini is the only player to have a buy-out clause - believed to be £22million - and, while Moyes' move to Old Trafford may increase the likelihood of a bid for Leighton Baines, who has long been linked with United, the club will not do their former employee any favours on the transfer fee.
While Kenwright said the last couple of days had been tumultuous, he admitted he suspected this day would come as planning with Moyes about next season ground to a halt several weeks ago.
"It's been an extraordinary 24 hours - one which I wasn't prepared for yesterday morning," he told Sky Sports News.
"It's been a year now since David and I sat down and went through this season and next season and we've been planning for next season until very recently.
"David Moyes has always been my manager and I seriously hoped he would be manager next season."
Kenwright's suggestion he was not prepared most probably relates to the timing of United's approach more than anything, with chairman most likely thinking he would have to deal with the issue at the end of the season.
The chairman knew Moyes was seriously considering his future and it's believed that groundwork was being done should he decide to go.
A source said it was inconceivable any major business would not be prepared for the possibility one of their major executives leaving, although there was no suggestion the club had actively explored their options.
"We couldn't stand in his way let's be honest because he is out of contract," said Kenwright.
"It was his decision and he's made it."
Martinez has been the bookies' favourite for the Everton post for some time now but with an FA Cup final and a relegation fight on his plate at Wigan, the Spaniard said he would not be talking to anyone about any such move.
"At this moment in time it would be a waste of time,'' said Martinez when asked if he had been approached.
"The most important thing is to be as ready as we can for Saturday and then the two other finals we have in the league after that.
"It is the peak time for us. We want our fans to be proud of us and that is what we are fighting for.
"What goes around on the outside doesn't affect us. We won't lose any focus.''
Speaking before Moyes' departure, the former QPR, Manchester City and Blackburn boss said: "It's obvious if one manager leaves there is an opportunity for other managers who are currently out of work, which includes myself.
"It (Everton) is a great club, a club I had the fortune to play for and I really enjoyed my time there. Whoever gets that opportunity it is a really big club and really big shoes to fill.
"It's an opportunity for somebody and I back myself for most jobs in the Premier League. It's a big job, there's only 20 jobs available and everybody wants to work in the Premier League."