Vincent Kompany’s men dominated the Championship last season and got promoted to the Premier League in a roaring fashion.
The Burnley boss is looking to build a squad that will be good enough to survive in the Premier League and has already brought in four new signings.
Clarke also enjoyed a good campaign and was a key man as Sunderland reached the playoffs; Burnley noted his displays and are keen.
Losing the winger would be a blow for Sunderland, but Burnley are continuing to explore taking Clarke to Turf Moor.
The former Tottenham winger is considered an exciting talent at the Stadium of Light and Tony Mowbray will lean on him heavily if he stays.
The Black Cats do not want to lose him and want Clarke to be part of a squad that could again challenge for promotion.
However, with Burnley still keen it remains to be seen whether Sunderland manage to keep him in the face of a concrete offer from the Clarets.