Franco Smith's side are guaranteed a top-four finish with one game remaining - at home to Zebre - next Friday.
Warriors, currently fourth, still have an outside chance of a spot in the top two which would also secure a home semi-final should they make it that far.
Their quarter-final opposition will be confirmed on 1 June once all fixtures are played.
Glasgow sit three points behind leaders Munster, who host Ulster on the final day, and all of the current top four could still finish at the summit.
Being guaranteed a top-four spot also means Smith's team will again compete in the Champions Cup next season, having made it to the last 16 this term before losing to Harlequins.