Journalist Paul Joyce, who is known for having decent Everton contacts, claims the Toffees had hoped to reach the end of the season before making a decision on the Spaniard's future.
However, the nature of Saturday's capitulation against the Foxes and the soaring levels of discontent and anger among the supporters may have forced their hand.
The report claims that new majority shareholder Farhad Moshiri and the board will also meet to discuss potential managerial replacements. Frank De Boer, Ronald Koeman, Joachim Low, Manuel Pellegrini and David Moyes are reportedly on their shortlist.
In the short-term though the sacking of Martinez and appointment of an interim coach may avoid outright mutiny from the fanbase at Goodison Park on Sunday.
The game will represent Tim Howard's final appearance in an Everton shirt after a decade of service while the likes of Leon Osman and Tony Hibbert may also be making their Goodison farewells.
They deserve a fitting send off from the club's supporters not tainted by the anger and vitriol directed at the club's manager.
I can understand the board's thinking by trying to wait until the end of the season before making a decision. But it seems the situation has deteriorated to such an extent any delay will only make things worse.