Dyche is the longest-serving boss in the English Premier League, having taken the reins at Turf Moor in October 2012, but he is understood to be on the radar of chairman Steve Parish as Roy Hodgson nears the end of his Selhurst Park contract.
The former England manager's deal is up in the summer and the Burnley boss is highly-regarded by the Palace hierarchy, with John Terry (5/2); Frank Lampard (7/2), and Lee Johnson (14/1) also among those linked with the Eagles.
Should Dyche be tempted south, Burnley will turn their attentions to Wilder, according to a report in The Sun.
Despite the Dyche link Eddie Howe – who had a brief spell managing Burnley – is the frontrunner for both the Celtic and Crystal Palace jobs, according to some latest odds.
The ex-Bournemouth boss is priced at 7/5 for the Hoops post, and 9/4 to take the reins at Selhurst.
Wilder was linked with Celtic earlier this year and despite the most recent odds suggesting he has fallen out of favour, the 53-year-old is believed to be on a shortlist that Parkhead chiefs are putting together, along with Howe and former Sunderland boss Roy Keane.
If Dyche does leave Turf Moor for Palace and Burnley make a move for Wilder, that could leave Celtic short of options as they seek a long-term successor to Neil Lennon – or it might increase Howe’s chances of landing the Hoops job.