Stringer finished the game but suffered a calf injury and his progress will be monitored though the expectation is that both players will be fit for consideration.
The same applies to veteran prop Marcus Horan who sustained a facial cut playing for Shannon against Young Munster in their Ulster Bank League opener.
Paul O'Connell (back), Johne Murphy (knee) and Luke O'Dea (ankle) are all expected to take a full part in training this week.
Ian Nagle (shoulder) did likewise last week but will be given a week or so before being made available for selection, and Cathal Sheridan (hand) and Ivan Dineen (groin) are also looking at a return within the same timeframe.
Reflecting on the performance against the Ospreys which saw them concede three tries, Munster boss Rob Penney said: "If we turn up and play, we are capable of being a competitive unit. If we don't turn up that's the sort of performance we'll get.
"We didn't bring anything. For some reason we were flat, we lacked the intensity and physicality that we've had the last few weeks.
"The Ospreys did bloody well and beat us up a bit. They came to play and we couldn't match it. What they brought was what we needed to have a bit of.
"We have been working really diligently and endeavouring to do the right thing by the group, so we'll just have to play the cards we are dealt."