According to The Telegraph, Everton approached Mourinho to invite the Portuguese coach to coach, but was immediately refused.

Last night, Everton officially announced because Benitez was dismissed, and now the club has entered the process of finding a coach.
The Telegraph pointed out that toffee approached Roma boss Jose Mourinho after firing Benitez to invite him to coach, but Mourinho immediately declined the offer because he focused on his job at Roma.