Palace have not yet appointed a replacement for Sam Allardyce, who took the surprising decision to stand down from his role at Selhurst Park despite keeping the club in the Premier League last season.
Mauricio Pellegrino and Frank de Boer have both been linked with the position, but according to the London Evening Standard, Dyche is also in the running, and the Burnley manager is interested in holding talks over the role.
Dyche has been at Burnley for four and a half years, which makes him the seventh longest-serving manager in England. He led Burnley to Premier League survival last season, and it is understood that the 45-year-old is now ready to move on.
It has been suggested that Palace would have to pay £1m in order to free Dyche from his Burnley contract.