Everton are looking for a new manager after sacking Rafael Benitez, an appointment that split opinion when it was made in the summer.
Benitez paid the price for a poor run of form and has been shown the door, leaving Everton hunting for a new manager to take charge.
Former Toffees boss Martinez, who is now the Belgium coach, was the Everton board’s first choice in the summer, before the owners appointed Benitez.
And the Spaniard retains strong support inside the Everton boardroom.
The club are though claimed to still be far off any final decisions being made about the next manager.
Martinez’s Belgium have reached the 2022 World Cup finals and it is unclear if he would be willing to leave his national team post before the tournament to answer the call from Goodison Park.
Former Everton stay Wayne Rooney, who is winning plaudits for his work at Derby County, has also been linked with the post.