Sunderland are understood to be interested in Dyche becoming their new manager after Dick Advocaat declined the chance to make his interim role permanent, having kept the club in the Premier League.
Dyche, who was unable to avoid relegation with Burnley, is currently on holiday and the Clarets have not yet received a formal offer for his services from the Black Cats.
But Warburton, a close friend and former colleague of Dyche at previous club Watford, would top Burnley’s list of successors and Sky sources understand Warburton would be interested in the role.
Warburton, whose contract at Brentford was not renewed following a disagreement about changes to the club’s management and recruitment structure, is hoping to continue working with former assistant David Weir and the pair are understood to have spoken to Scottish championship club Rangers.
The 52-year-old Warburton is remaining patient about his future despite a determination to return to management as quickly as possible and his former sporting director at the Bees, Frank McParland, has already taken up the same role at Burnley.
McParland was placed on gardening leave by Brentford when the club announced in February that his services, along with Warburton’s and Weir’s, would not be required beyond their contracts, which expired on May 30.
McParland also worked with Dyche and Warburton at Watford, before spells in various recruitment and coaching capacities at Bolton and Liverpool.