The Dutchman would apparently welcome a move to Goodison Park..
The Spaniard certainly appears to have lost the support of Everton fans following a season which will most likely see them finish in the bottom half of the Premier League table.
Given the amount of talent he has at his disposal on Merseyside, Martinez is perceived to have underachieved in a major way this season, despite reaching an FA Cup semi-final.
De Boer is regularly linked with an Ajax exit but it never appears to materalise, with the 45-year-old in charge of the Eredivisie giants since 2010, in which time he has won four Dutch top-flight titles.
He certainly has a strong CV, and Everton supporters made their feelings clear about the potential interest.
@ReadEverton I'd be happy with David Brent at the minute, he'd still do a better job than the deluded leader we have at present— Everton Ian (@everton_ian75) May 8, 2016
@RBMersey hasn't he just won 4 titles on the bounce haha how can people not want this man in charge of our club— Michael Bagan (@BaganMichael) May 8, 2016
Whether he would be a gamble or not, having the likes of Frank de Boer wanting to manage us shows that we can and should set the bar high.— Everton Aren't We (@EvertonArentWe) May 8, 2016
@LivEchoEFC and watch bungling bill go for O'Neill, Hughes or Lennon— treboreuk (@treboreuk) May 8, 2016
Martinez replaced David Moyes at Goodison three years ago, but the former Wigan coach has not really achieved the same level of consistency as his predecessor did - and he might well pay the price.