Mirallas, 27, has been with the Toffees for three years now having joined from Greek side Olympiacos in 2012, and has become a valuable player at Goodison Park.
The Belgian international winger has hit 28 goals in 106 games for Everton, including 11 goals last term - but speculation surrounds his future on Merseyside.
The Sun report that Everton have held discussions with West Ham over a deal to send Mirallas to Upton Park this summer, with new Hammers boss Slaven Bilic looking for reinforcements.
However, the report also states that Everton have decided not to sell Mirallas to West Ham, and will instead enter talks over a contract extension with the former Saint-Etienne star in the near future.
The news would serve as a huge blow to West Ham, who certainly need a new winger if they are to play in Bilic's preferred 4-2-3-1 formation in the upcoming season.
Ideally, Bilic could play Diafra Sakho as the lone striker, with Dimitri Payet roaming behind, getting into space to create chances and have shots on goal himself.
Down the right would be Ecuador international Enner Valencia, who possesses the pace to take players on and beat them in behind, leaving a space on the left hand side.
Mirallas, who can beat full backs as well as score goals, would have been ideal on that left hand side, cutting in on his right foot to add another attacking option for Bilic - but with Everton seemingly set to keep the player, West Ham may have to look elsewhere for reinforcements.