The 25-year-old, who has one Premier League winners medal to his name, has spent this season on loan with Aston Villa, scoring three goals in 38 games. He helped the Birmingham-based club to the FA Cup, and head coach Tim Sherwood has indicated to the Guardian that he is keen to see him remain at Villa Park on a permanent basis.
The Daily Mirror has also indicated that a host of other Premier League clubs are interested in the England international, with Tottenham, West Ham and Sunderland all tracking his availability, but it appears as if the Toffees have made the first concrete moves to sign him.
Cleverley worked with Everton boss Roberto Martinez during a loan spell with Wigan in the 2010/11 season, and the Spanish coach is keen to wrap up as much business as possible in the next few weeks to get ahead of their rivals in the transfer market.
The report states that Cleverley could give a decision on his future in the next two weeks, and with Everton the only club to formally submit an offer for his services, the Merseyside outfit look to be in pole position for his signature.