Everton sacked coach Roberto Martinez on Thursday, bringing an end to his three-year reign at the club, following a disappointing campaign in which they finished 11th in the English Premier League (EPL).
Reports this weekend claimed Everton had made contact with Mourinho to discover if he would be interested in taking over at Goodison Park.
Sky Sports reported that Mourinho has kept his options open and it is understood he would prefer a move to Manchester United if they decide to make a managerial change, replacing Louis van Gaal this summer.
Mourinho expected to be at a top club next season, and is relaxed about the fact he doesn't yet have a deal agreed at any club.
The former Real Madrid coach remained long odds-on to be United's next boss, and said last week he believes he will be at a club in time to start this pre-season.
When asked about United in Mexico City last week, the Portuguese said, "I don't know. I know nothing about it really. I don't have a club. In July, I will be back. So we are in May. May to July is nothing. I keep enjoying my life which I'm doing, keep enjoying my family. But in July I am back."
Mourinho and his agent Jorge Mendes will consider all viable options as the Portuguese plans his return to management.