The Clarets now find themselves without a win in their last 16 league games following their latest setback, a 2-0 defeat to fellow strugglers West Ham at the weekend.
Pressure continues to mount on under-fire boss Parker, with the club heading towards another relegation back to the Championship.
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They take on a Palace side that ended their run of poor form with a 1-0 win against rivals Brighton on Sunday afternoon.
Both sides have some injury concerns to contend with heading into Wednesday night’s encounter, so here's an early look at the team news for both outfits:
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5. Josh Cullen (Burnley) - out
The skipper is facing around nine months on the sidelines after suffering a devastating ACL injury in the game against Everton. (Photo by Molly Darlington/Getty Images) Photo: Molly Darlington
6. Connor Roberts (Burnley) - out
The Welshman, who has yet to feature this season, is still some way away from returning from an Achilles injury. (Photo by Alex Livesey/Getty Images) Photo: Alex Livesey
7. Mike Tresor (Burnley) - out
The winger is facing a number of weeks on the sidelines after suffering an ankle injury during the game against Newcastle just before New Year. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
8. Axel Tuanzebe (Burnley) - doubt
The defender missed the weekend’s defeat to West Ham with an Achilles injury, having been hooked off at half-time against Sunderland. (Photo by Molly Darlington/Getty Images) Photo: Molly Darlington