The Eagles slowed down and reset their recruitment process after missing out on top target Marco Silva, believing the other available candidates to all be a tier below the Portuguese.
But Dyche has been in the conversation since day one and has shown a keenness to leave Turf Moor and move south again, having previously impressed at Watford.
Palace chairman Steve Parish, with input from his American co-owners, has crunched the numbers on a wide range of candidates.
Mauricio Pellegrino is keen to work in England and represents an intriguing candidate after his work with Alavés this season, but he left the club to resolve some personal issues in his native Argentina and the job may come too soon for the former Liverpool defender.
Garry Monk and Roy Hodgson are not understood to be high-priority candidates, while Roger Schmidt was on an early longlist but has not received further contact.
Dyche is on holiday currently and is understood to have a release clause of £1m.
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