The 28-year-old is expected to move to Marseille on a season-long loan deal which could include an obligation to buy for a fee of £3.4million.
The Frenchman spent last season on loan at Brentford, where he scored eight goals in 31 appearances.
He is into the last 12 months of his contract at Goodison Park after signing from Brighton in August 2022.
The move would see the Frenchman join a revamped team in Ligue 1 after the appointment of manager Roberto De Zerbi following his departure from Brighton this summer.
Maupay would join a host of ex-English league talent, including Mason Greenwood, Jonathan Rowe, Pierre-Emile Hojbjerg and Ismael Kone.
It remains unclear whether Everton will sign a replacement striker after manager Sean Dyche said the club had ‘no money’ as they seek to complete a takeover.
But a forward signing, potentially on loan, will be among the club’s priorities before the transfer deadline at 23:00 BST on Friday.
On Sunday Maupay responded to a video showing a group of supporters verbally abusing Toffees players at London Euston train station.