The Blues right-back was forced to sit out last weekend's local derby game against Aston Villa because of a thigh strain.
However, manager Alex McLeish does expect Carr to have recovered in time for the match against The Tigers at The KC Stadium.
McLeish could also include central defender Scott Dann in his squad as he is without Franck Queudrue, Martin Taylor and Liam Ridgewell through injury.
Dann has made two appearances for the Blues reserves side in an effort to step up his match fitness following two months on the sidelines with the thigh injury he sustained in the pre-season match against Dagenham & Redbridge.
Elsewhere, centre-back Giovanny Espinoza face's a race against time to be fit for Saturday's match as he sustained a groin strain in the Reserves' 1-1 home draw against Fulham on Monday night, as does left-back Gregory Vignal, who has missed the last six games with the hamstring injury he picked up in the home win against Portsmouth in August.
For a detailed head-to-head between the two sides, click here