The 31-year-old joined his boyhood club on a free deal from Manchester United last week, and the report claims that he still hasn't given up hopes of making it to World Cup next year.
Starsport quotes a source: "Wayne loves playing for England and nothing has changed. He still thinks he should be in the team and wants to go to Russia.
"He realises he needs to earn the right to be back in the manager's plans, but thinks he can do this at Everton. It was a big part of his decision to go back."