The 24-year-old was associated with a move to Leeds United this summer, but those links have cooled after the Whites signed Junior Firpo from Barcelona.
Burnley, though, remain interested in acquiring the Ivory Coast’s international’s services from Lyon and bringing him to the Premier League ahead of the new season.
The Clarets are said to have approached Lyon to enquire about the possibility of signing Cornet, but face competition from German top flight club Hertha Berlin.
And according to French sports daily L’Equipe, the left-footer prefers joining the Bundesliga outfit rather than plying his trade for Dyche’s side in the Premier League.
Lyon are claimed to want €13m for Cornet’s sale and while Burnley are not put off by the asking price it remains to be seen if they can convince him of a move to Turf Moor.
Hertha Berlin have been keen on acquiring the services of the former Metz star for several months and could step up their interest in the player soon.
Cornet scored four goals and provided six assists from 39 appearances across all competitions for Lyon last season.
