Kilmarnock chairman Michael Johnston will resume discussions with Allan Johnston on Wednesday over the manager's position.
Some of Kilmarnock's most prominent backers have told chairman Michael Johnston they can only support the club if he vacates his position.
Hibernian have appointed Jimmy Nicholl as assistant manager after he left his role with their SPL rivals Kilmarnock.
Kenny Shiels says he is "heartbroken" to leave Kilmarnock and admits his love for the club clouded his judgement.
Manager Kenny Shiels has left Kilmarnock by mutual consent, the club has confirmed.
Kilmarnock will reportedly tell Kenny Shiels his two-year tenure as manager at Rugby Park is over later on Tuesday.
Kilmarnock have denied rumours that boss Kenny Shiels has been sacked - and reiterated his position will be discussed at a meeting this week.
Kenny Shiels will have his position reviewed as Kilmarnock manager after he was handed a four-match ban for outspoken media comments.
Kilmarnock manager Kenny Shiels has been handed a four-game ban, with two matches suspended, after bringing the game into disrepute.
Rangers have signed Scotland international goalkeeper Cammy Bell from Kilmarnock for next season.
James Dayton has agreed to join Oldham Athletic on a two-year contract after rejecting a three-year deal at Kilmarnock.