The Clarets have been without a manager since Eddie Howe returned to Bournemouth due to family reasons earlier this month.
Youth team coach Terry Pashley took over as caretaker boss and led the Championship side to two consecutive wins before a 4-0 weekend loss at leaders Cardiff.
According to various reports Dyche attended the game as a guest of Cardiff manager Malky Mackay, whom he worked under at Watford.
And Press Association Sport understands the 41-year-old is due to arrive in Burnley on Monday for a tour of the club's facilities before signing as manager tomorrow.
He will be accompanied by former Nottingham Forest midfielder Ian Woan, who served as his assistant at Watford last season.