McGrath was treated earlier this year for testicular cancer but has made a good recovery and could yet take the field for the Premier County against the Tribesmen.
“Noel is progressing well,” said O’Shea last night.
“It’s a serious thing so you just have to wait and see how he goes and what happens.
“He’s been hurling away with us and he has played for his club a couple of times. It’s great credit to him in terms of it’s good to get back doing things he likes doing, like any of us.
“I think that’s been the big thing for us, we haven’t been thinking really about the game or competitively or whatever, it may turn out like that, hopefully, but the big thing was to get him back in an environment where he’s happy. That was the main thing for us.
“He’s in the mix (for Galway).”
Tipperary have a full squad to pick from, with key defender Padraic Maher recovering well from a knock in the Munster final win over Waterford.
“I don’t think there is anybody definitely out,” said O’Shea.
“Padraic has been injured but we are hopeful he will be okay. We’ve had ongoing little minor issues with Michael Cahill and Paddy Stapleton, just little bits and pieces here and there but we’re hopeful that by the middle of next week everybody should be okay. I think it (Padraic Maher injury) was AC-related. The physio looks after all the terminology but we’re hoping he’s okay. Has he trained? No, but we’re hopeful, and that goes for a few of them.”