The Toffees are on the lookout for a new manager having dismissed Rafael Benitez from his post owing to a terrible run of results in the Premier League.
A 2-1 defeat away at relegation candidates Norwich City at the weekend meant Everton have only one win to their name in their last 13 top flight outings, and Benitez was relieved of his duties on Sunday, less than seven months into his spell.
Former Toffees boss Martinez is among the leading contenders to replace Benitez, with the likes of Derby County boss Wayne Rooney, ex-Napoli coach Gennaro Gattuso and Everton assistant manager Duncan Ferguson are among the other names.
Martinez was among the names considered by the Everton hierarchy in the summer before club supremo Farhad Moshiri pushed to sign Benitez.
And the Merseyside giants are keen to have the 48-year-old take over at Goodison Park for a second time, having managed them between 2013 and 2016
Martinez, who is currently coaching the Belgium national side, would love to return to Everton for a second stint as he has great admiration for the club.
However, as it stands Martinez signing for Everton before the international tournament is rated unlikely as the Belgian FA are unwilling to let him leave his current job.
Martinez’s first season in charge of Everton saw them securing European competition with a record points tally, but his next two terms were underwhelming, with the club finishing in 11th on both occasions.
It remains to be seen whether Martinez will be handed an opportunity to lead the Toffees again as they continue to struggle just above the relegation zone.