Piutau limped off with a dead leg midway through the second half of Ulster’s first win in five outings, over Edinburgh last Friday night.
However, the big All Black is already back training and supremo Les Kiss is confident he and a number of other frontline players will be available for selection.
Rome hat-trick hero Craig Gilroy, along with Tommy Bowe, Luke Marshall, and Stu McCloskey, have been released from Ireland duty, while Ruan Pienaar was looking sprightly on the training paddock yesterday. Skipper Rob Herron, Darren Cave, and fly-half Brett Heron will also be looking to put up their hand for selection, though Stuart Olding is out for a couple of weeks with an elbow issue.
Ulster led 24-10 at the interval, but failed to score on the restart as Edinburgh closed to within six points.
Kiss, though, wasn’t overly concerned by that statistic.
“I put that in the compartment and forgot about it,” he said. “We have gone through it. We have looked at a couple of key things that could have made a massive difference, but there were a lot of good things in the first half that we worked on in the previous couple of weeks that came through for us.
“When you look at it closely, Edinburgh really came back at us. I have to take my hat off to them, as they pushed us and we did not respond the way I would have liked, but we got the result.
“The dressing room is already different,” said Kiss of the mood in the squad after breaking their four-game losing streak. “We have also accepted that we did not finish the game as well as we would have liked, but we’ll try and build on the things we did well in the first half,” said Kiss, as he looks forward to a Glasgow side who will have some of their in-form Scotland players back on duty.
“We are going to need it. Glasgow disappointed themselves losing to Scarlets at home last weekend. They will be keen to get something out of this game, so we need to be able to put another wee bit of a layer on what we did in the first half against Edinburgh.”
The encounter is a crucial one for both sides, as they chase a top-four place, which would secure a place in the semi-final play-offs.
Glasgow lie fifth in the table, three points ahead of Ulster, who have a game in hand over the Scottish side.