Maupay has scored just once since joining from Brighton & Hove Albion last August, and has fallen down the pecking order since Sean Dyche arrived as manager.
Despite the injury to Dominic Calvert-Lewin, Maupay still finds himself behind Demarai Gray and Ellis Simms in Dyche's plans.
In an interview with Tuttomercatoweb.com, Maupay's agent Federico Pastorello hinted that his client could make a move to Serie A in the foreseeable future.
Pastorello revealed: "Salernitana wanted him, but Everton got the deal done then changed the coach, we'll see in June."
Maupay has played in England for six years since joining Brentford from Saint-Etienne, but Pastorello believes the Frenchman could be ready for a new challenge.
"There could be options in Serie A, Neal is open to joining Italy," he added.
The club initially linked with Maupay, Salernitana, remain in a relegation battle in Serie A, but four games without defeat have moved them eight points clear of trouble.