While Maxime Esteve is back from injury and Axel Tuanzebe, Hannibal and Lyle Foster have now all returned from AFCON, the Clarets’ squad continues to be stretched.
Parker has often made wholesale changes in cup competitions – and with Burnley’s priority being Premier League survival, you’d expect the same to be the case this weekend.
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But the Clarets aren’t the only side with selection issues, with Millwall also likely to be without a number of key names.
Both sides have some injury concerns to contend with heading into Saturday’s encounter, so here's an early look at the team news for both outfits:
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5. Connor Roberts (Burnley) - out
The Welshman, who has yet to feature this season, is facing months on the sidelines after suffering a setback in his return from an Achilles injury. (Photo by Alex Livesey/Getty Images) Photo: Alex Livesey
6. Mike Tresor (Burnley) - doubt
The winger has missed Burnley’s last two games with what was initially perceived to be a minor knock, but the pain has since persisted. Photo: Kelvin Lister-Stuttard Photo: Kelvin Lister-Stuttard
7. Joe Worrall (Burnley) - doubt
The defender has missed Burnley’s last four games after picking up a “niggle” in training. Like Flemming, faces a race against time to prove his fitness. (Photo by Matt McNulty/Getty Images) Photo: Matt McNulty
8. Josh Coburn (Millwall) - doubt
The striker could make his return from a quad injury that has kept him out of action since the October international break. (Photo by Richard Pelham/Getty Images) Photo: Richard Pelham