Argentine coach Marcelo Bielsa wanted to work with Everton's Under-21s team before taking over the seniors in the summer.
Bielsa was approached by Everton this week to replace the fired Frank Lampard as head coach.
However, The Times states that Bielsa suggested a model that would see an interim take charge of the first team.
He would then work with the under-21s and the club's academy until the summer.
After then getting a chance to make transfers and go through pre-season, Bielsa would take over the first team.
Everton appear to be heading in the direction of hiring ex-Burnley boss Sean Dyche instead.