Zigic has sat out of the club's last two games with a knee injury and was facing a late fitness test prior to Saturday's postponed clash at Barnsley.
The Serbian will continue to be monitored ahead of Hull's visit, as will fellow striker King who has been playing through the pain barrier having struggled to fully shake off a groin complaint.
Midfielder Guirane N'Daw has been ruled out with the hamstring injury he sustained early on in the 1-0 defeat to Portsmouth last Tuesday.
Otherwise, manager Chris Hughton has a full-strength squad to select from as Blues look to extend their unbeaten record on home soil in the league this term and stretch the current one-point gap between themselves in third and the sixth-placed Tigers.
Hull manager Nick Barmby is expected to select his starting line-up from an unchanged squad.
Barmby has no new injury or suspension problems following his side's 3-0 success over Doncaster on Saturday - the Tigers' biggest win of the season.
Hull have kept clean sheets in their last four league games and Barmby is unlikely to consider any changes at the back.
Midfielder Seyi Olofinjana is hoping to be included in the squad after missing out altogether against Doncaster.
The big Nigerian made his first league appearance for Hull in nearly a year when stepping off the bench in the recent home draw with Doncaster after a long-term knee injury.
Striker Matty Fryatt scored his first goal since early December at the weekend and is expected to continue his partnership with Robbie Brady.
Source: PA
Source: PA