The Clarets have shown an interest in signing the former Tottenham winger but negotiations with Sunderland have not gone according to plan.
Burnley have failed with a bid of £10m for the player and Tony Mowbray is expecting to keep the winger at the Stadium of Light next season.
Clarke has made it clear that he wants to grab the opportunity to play in the Premier League and would be keen on the move.
Burnley are about to sign Hoffenheim winger Jacob Bruun Larsen on loan but the club are still interested in Clarke.
Kompany is driving the club’s interest and he is very keen to take the winger to Turf Moor in the ongoing transfer window.
Burnley have several other targets but Clarke is a player the manager likes and he is keen to sign him.
It remains to be seen whether the Clarets make an improved offer to temp Sunderland into selling him.
