The Spaniard has come under increasing criticism this season after a mediocre Premier League season that has left them 12th in the table.
According to the reports, Martinez failed to take training on Thursday ahead of the final game of the season against Norwich City on Sunday while the BBC and Sky Sports television said he had been sacked.
The team reached the semi-finals of the League Cup and FA Cup but Martinez's side have under-performed in the league despite boasting a squad many regard as Everton's best for many years.
Everton have won just one of their last 10 league games and some fans turned on the manager after they lost 4-0 to local rivals Liverpool last month.
Banners calling for him to be sacked have appeared at recent games and a protest was planned for Sunday's finale.
Martinez gained a reputation for an attractive football style in previous stints at Swansea City and Wigan Athletic.
He won the FA Cup with Wigan but the club were also relegated in the same season before he joined Everton in 2013, taking over from David Moyes.
Everton finished fifth in his first season in charge but struggled to back that up last term when they were down in 11th.
They have managed only five home league wins this season.
Original source: Martinez sacked by Everton - reports