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.