Cornet has been pushed down the pecking order at West Ham and his prospects of game time could worsen with the Hammers looking to bring in another attacker.
The former Lyon winger could have an escape route as Sean Dyche wants to take him to Goodison Park.
Dyche wants attacking signings and, according to French journalist Ignazio Genuardi, talks are taking place with West Ham over Cornet.
The Toffees are having to watch their finances closely, but they have just splashed the cash to sign striker Beto from Udinese.
Dyche wants more and is keen for Cornet to be added to the ranks.
Cornet caught the eye when he initially moved to the Premier League to join Burnley, but he has struggled to convince David Moyes to give him regular game time at the London Stadium.
It is unclear if Everton are looking to sign Cornet permanently from West Ham or loan him.
The 26-year-old has played just one minute in the Premier League this season.
