Hooker Flannery's calf injury has been resolved but a subsequent hamstring injury has him sidelined with no definite timescale for a return to full training.
Centre/winger Earls is another player the Munster management will wait on for a further scan before determining when he can resume training.
Earls spent the day alongside Murphy working with the province's fitness staff. Murphy's ankle injury has been sorted but he has been troubled by a hamstring problem more recently.
His fellow centre Mafi is expected to be back for Magners League round 3 which means he should be in contention for the start of European action.
Prop Dave Ryan is out with a quad strain picked up in training, while backs Tom Gleeson and Declan Cusack are struggling with groin injuries.
Back rower James Coughlan took a bang to his shoulder in the province's opening pre-season game against Leicester Tigers and it is hoped he will resume full training next week.