Central defender Morgan missed Saturday's vital win over Millwall with a twisted knee and he remains a doubt.
The Millers have an otherwise full squad to choose from as they chase a fifth game unbeaten on home soil.
Steve Evans could be tempted by changes and Adam Hammill will fancy a starting berth after his cameo off the bench at the weekend.
Cardiff will be forced into making at least one change for the trip to the New York Stadium.
Peter Whittingham will miss out after seeing red in the loss to Wolves, which means he starts a one-match suspension.
Conor McAleny could be the man to come into the side after an appearance from the bench on Saturday, but Tom Adeyemi, Stuart O'Keefe and Joe Ralls are also contenders.
Matthew Connolly and Lee Peltier look set to continue at full back, with Fabio still struggling for fitness with a calf problem.
MATCH FACTS
Head-to-Head
- The earlier meeting this season ended as a goalless draw at the Cardiff City Stadium in December.
- Cardiff are unbeaten in the last five meetings, winning two. Rotherham's last win was 1-0 at home in the old Division Three in March 1999.
- Rotherham are unbeaten in their last six meetings at home, winning three. Cardiff's last win there was 2-1 in the old Division Four in February 1992.
Rotherham
- Rotherham won 2-1 against Millwall on Saturday - their first win in five games.
- United have won three of their last four home games, drawing the other. Their last defeat at the New York Stadium was 2-0 against Bournemouth on 17 January.
Cardiff
- Cardiff have won only one of their last 10 games in all competitions. Their only win since mid-January was 1-0 at Wigan in the Championship on 24 February.
- City are unbeaten in their last three away games, winning once. Their last defeat on the road was 2-1 at Middlesbrough on 20 January.