Glasgow are lying ahead of the Borders in the Celtic League, but they are only separated by four points. The Warriors, on the other hand, are keeping a close eye on the Ospreys and the Blues.
"Our number-one priority is to qualify for Europe, there is no other agenda," said Warriors coach Lynn Howells.
"I would have thought Glasgow would have much the same attitude as us."
On Glasgow, he said "We found them very difficult to play against and their forwards certainly gave us plenty to think about.
Glasgow's backs coach agrees "While we would like to win all our remaining games, we really have to target the two home fixtures," said Sean Lineen.
"We will be the underdogs in all four games and we were desperately poor at home to Munster last time out, so we must re-establish our previous home form immediately."
“I think it is going to be pretty tight – there is a lot of hunger there as our sole goal is to secure a Heineken Cup place for next season.
"We have played the Warriors twice already this season – with one win and one loss – and when we went to their place we knew we had to get stuck into them, there is this real fear factor you are going to take a hammering when you go to Wales.
“There wasn't much free flowing rugby from either side on those occasions and, while we would like to win all our remaining games, we really have to target the two home fixtures."