The 42-year-old is believed to be discussing the terms of a severance package with club officials in the wake of Wednesday night's 3-0 defeat to Sunderland at the Stadium of Light
Martinez had dismissed speculation over his future after the defeat in the north-east, insisting the players were "100 per cent" committed to his remaining in charge
But their latest shambolic display suggested differently and the club's board, including new majority investor Farhad Moshiri, have decided to act ahead of the match against the Canaries.
The timing of the impending departure will inevitably fuel speculation over a move for Frank de Boer, who announced he was leaving his role as Ajax coach on Thursday morning.
Outgoing Manchester City boss Manuel Pellegrini and former boss David Moyes have also already been installed among the favourites to succeed Martinez at Goodison Park.
Martinez joined Everton in 2013 after leading Wigan to an unlikely FA Cup triumph, and took them to 11th place in his first season in charge.
But the Spaniard faced growing criticism this season for failing to bring the best out of a squad including Romelu Lukaku and highly-prized pair John Stones and Ross Barkley.
Defensive issues in particular saw the side slump in the new year, including a 4-0 derby defeat to Liverpool, and last month's FA Cup semi-final defeat to Manchester United effectively ended any hopes Martinez had of retaining his role beyond the summer.
Amid mounting discontent, Martinez saw his side crumble 3-1 at champions Leicester last Saturday before Wednesday night's equally miserable performance against Sam Allardyce's men.
Fans had been planning to protest at the club's scheduled Player of the Year dinner in Liverpool on Thursday, but it now seems highly unlikely that Martinez will attend.
Source: PA