The Daily Mail says Tom Heaton has only recently regained his No 1 spot and did very well as Dyche's side collected 21 points from his first nine games back. Heaton's form earned him a call-up to Gareth Southgate's England squad.
But Burnley have now lost four games in a row, conceding 10 times, to slip to 17th. They are two points above Cardiff having played a game more and Dyche is thinking of bringing back Pope for the visit of Wolves on March 30.
The 26-year-old, who starred for Burnley last season and won a place in Southgate's World Cup squad, lost his place after picking up a shoulder injury in the Europa League tie at Aberdeen last July. He recovered in December but has only played in Burnley's two FA Cup ties since.
Joe Hart has been on the bench in Premier League games.