The Daily Star says Martinez became favourite for the Goodison job as soon as David Moyes quit to take over at Manchester United.
He said: "It will be maybe the right time for a fresh challenge.
"The right time for a fresh man to come in and take the football club to a new level. I take real pride in building football clubs and I've done that previously when I left Swansea.
"It was the right time to leave and I knew the club was ready to kick on."