Parrish limped out of Saturday's entertaining 1-1 draw against Bristol Rovers after picking up a thigh injury.
Robbie Threlfall replaced him during the first half and is expected to deputise at full-back.
Andy Wright must serve another game on the sidelines with suspension.
The midfielder received two yellow cards in the Shrimps' 1-0 win over Port Vale but had an extra match added to his one-game suspension for reacting angrily to the referee's decision.
Jack Redshaw is poised to start once more having netted his 11th goal of the season at the weekend and boss Jim Bentley is demanding more from the diminutive striker.
"He's just got to have that hunger," Bentley told the Morecambe Visitor. "He's played well and looked good on the eye and caused their centre halves problems.
"He's had four shots on target and scored one, seen a couple cleared off the line and popped up everywhere, but he's got to have that hunger in his game."