While not a direct recommendation for the job, it appears that the current manager of the Spain football team Vicente Del Bosque has included Everton manager Roberto Martinez on the list of managers that could replace him. That list also included former Liverpool manager and current Newcastle United boss Rafa Benitez and Julen Lopetegui, who was in charge at FC Porto until earlier this year. It seems like a long shot for Martinez, but Del Bosque will be leaving after Euro 2016 so the job will be available.
Of that list Lopetegui is currently without a job and Benitez has just been hired at the Toon. If it was just those three on the final list I think it's not a reach that Spain could call on Martinez to take over the national team, especially since Pep Guardiola has also signed on at Manchester City.
Although Martinez is under contract until the summer of 2019 it's apparent his playing style and attitude are coming up short with Blues fans and now even players appear to be stepping out against the manager. If rumors of John Stones interest in leaving this summer center on the manager then that just confirms the team would be happy to see him leave for the La Furia Roja job after this summer.
If the team doesn't force him to leave though, I'm not entirely sure he would be so quick to quit. Yes he left Wigan Athletic quite willingly to arrive at Goodison, but his reputation has taken a battering in England recently and leaving after such a down season could make finding a job much harder. We do have to remember though that he came to the Toffees after getting relegated with Wigan.