Tony Pulis' side can move level on points with the visitors to Selhurst Park, who have struggled lately after an impressive start to their Premier League return.
Steve Bruce's side occupies the relative safety of 11th place but a run of three straight league defeats, in which they have failed to score a goal, has narrowed the gap between themselves and the bottom three.
Palace, meanwhile, has climbed the table to 16th and a home victory Tuesday would underline the contrasting recent fortunes of the two sides.
When they met in November, City held a 10-point advantage over Palace, but if the London club can complete a league double over the KC Stadium outfit, it will draw level. And history is on the hosts' side, too, with Hull having returned winless from its last 10 trips to Selhurst Park - a record stretching back to 1986.
Barry Bannan's late goal settled matters in this season's meeting at Hull, when the visitors finished with 10 men following Yannick Bolasie's dismissal.
Both clubs were in action on Saturday in the fourth round of the FA Cup, with City earning a 2-0 win at Southend United, managed by its former boss Phil Brown, while Palace was beaten 2-1 at holder Wigan Athletic.
That defeat will allow Tony Pulis' men to focus exclusively on the fight for top-flight survival as Palace seeks to end its abysmal record of having been relegated from the Premier League on each occasion that it has competed in it.
Pulis masterminded a 1-0 victory over his old employer Stoke City last time out in the league, with Jason Puncheon atoning for his penalty miss against Tottenham by netting the decisive goal.
Hull was beaten 1-0 at Norwich City, a defeat compounded by Tom Huddlestone's late red card, meaning he missed the trip to Roots Hall.
The midfielder is likely to start against Palace, while Robbie Brady, who featured from the bench against Southend, will also come into consideration for his first league start since early December following a groin injury. James Chester (hamstring), Joe Dudgeon (knee) and Sone Aluko (calf) are all ruled out.
Much has been made of Palace's sizeable squad - described by one study as "the biggest in Europe" - and Pulis has relatively few injury concerns.
Kagisho Dikgacoi and Jerome Thomas (both calf) could return, while Cameron Jerome, who was ineligible to face his parent club Stoke in the previous league game, is set to start in attack. Defender Jack Hunt (ankle) and long-term absentee Glenn Murray (knee) remain on the sidelines.