Maupay is keen to move on from Brighton before the transfer window slams shut and several sides have shown interest in landing him.
The Frenchman is wanted by Fulham, who have been pushing to take him to Craven Cottage, but now Everton are in pole position.
The Toffees are in advanced talks with Brighton to get a deal for Maupay over the line.
It is suggested that Everton are hopeful that an agreement can be reached with the Seagulls for Maupay to make the move to Goodison Park.
There does though remain work to be done in the negotiations between the two clubs, with no final agreement reached.
Frank Lampard has been clear about Everton’s need to add attacking options before the transfer window slams shut next week.
Everton have been linked with a number of players, including Blackburn Rovers’ Ben Brereton Diaz and Southampton’s Che Adams.
