Martinez, who arrived from Wigan Athletic as David Moyes' replacement back in the summer of 2013, may have enjoyed a superb first season at Goodison Park - taking the Toffees to within touching distance of the top four - but it's been downhill from there.
After an 11th place finish last season, Everton are once again treading water in mid-table, and Saturday's 1-1 draw at Watford leaves the Toffees in 14th place, with only the bottom four clubs - Aston Villa, Newcastle, Sunderland and Norwich City - winning fewer games than Everton this season.
That has put Martinez's position in question, and fans protested against his reign on Saturday afternoon - and now, it's claimed that new shareholder Farhad Moshiri is keen to spark a change at Goodison Park by approaching Marcelo Bielsa.
Goal report that contact has already been made by Everton towards Bielsa, who has been out of management since leaving his post as Marseille manager last summer.
The 60-year-old is known as one of the most influential managers in the world, having played a part in the careers of Argentina boss Gerardo Martino, Tottenham's Mauricio Pochettino, former Chile boss Jorge Sampaoli and Manchester City's manager-to-be Pep Guardiola.
One of the most innovative managers around thanks to his famed 3-3-3-1 formation, Bielsa has earned the nickname of 'El Loco' over his career thanks to his outlandish methods, and he impressed as manager of Chile, Athletic Bilbao and Marseille before his exit almost a year ago.
Now, it's claimed that Everton have sounded him out for the job of replacing Martinez this summer, and the report also claims that Bielsa is interested in the role given that he has a dream of managing in England. Whether that claim is true or not remains to be seen, but expect to see plenty of speculation about the Goodison Park dugout this summer.
Would you like to see Bielsa replace Martinez?