It has been well documented that the 25-year-old's contract contains a £17.5m release clause, allowing any interested clubs this summer to trigger it and enter into talks for the player.
As a result, several Premier League sides are said to be interested in signing Cornet during the transfer window, but The Athletic are reporting that Everton are currently leading the race.
The report suggests that Frank Lampard's side are looking to find an agreement with Burnley over a potential deal, and whilst nothing has been confirmed as of yet, discussions are continuing.
Should he make the move to Merseyside, Cornet would become Everton's second signing of the transfer window, after James Tarkowski also made the move from the Clarets earlier in the summer on a free transfer deal.
Lampard is keen to rebuild an Everton side that narrowly avoided relegation from the top flight during the 2021-22 campaign, and has since seen Richarlison leave for Tottenham Hotspur.
While the Toffees survived the drop last season, Cornet and Burnley were not so fortunate, and as a result, the previously-mentioned release clause has become active.
Despite the disappointment on a team level, the Ivorian enjoyed a productive debut campaign in the Premier League, scoring nine goals in 26 league appearances after making the move from Lyon for around £13m last summer.