Midfielder Noble has served a one-match ban following his red card at Burton last week, while Morgan returns to the fold after a foot injury which has sidelined him since mid-November.
Boss Steve Evans will have to decide whether to tinker with his starting line-up after an impressive midweek win at Torquay that saw the Millers adopt a 4-4-2 formation.
Ben Pringle was dropped to the bench for the 3-1 victory at Plainmoor and will be eyeing a recall, as will on-loan Blackburn striker Jordan Slew.
Michael O'Connor still has two games to serve of his three-match ban for stamping against the Brewers while goalkeeper Scott Shearer is the only player in the treatment room.
The Millers, who occupy the final play-off spot, are unbeaten on home soil against their north Derbyshire rivals since 2007.