But the Premiership outfit's destiny in Europe is not in their hands even if they get what they want against Glasgow.
The English side, who were beaten finalists in 2011, do face the prospect of failing to reach the last eight of European rugby's premier tournament for the second successive season.
But they did manage a narrow 18-12 victory over Castres Olympique at Franklin's Gardens and after their win over Pool winners Ulster in Round 4 they have found some form with Dylan Hartley on song at finding his targets at line-out time.
Glasgow, who are second in the PRO12, have not won a game in Europe during this campaign and will want to transfer their domestic campaign to the Heineken Cup and sign off in style.
The Warriors will also be buoyed by the fact that Scott Johnson, the interim Scotland coach, has named 19 of their players in his 35-man training squad for the forthcoming Six Nations.
- Glasgow have slipped to seven successive Heineken Cup defeats - their worst run since 2005.
- Glasgow's last seven matches against English opponents have all been won by the home side on the day.
- Northampton have won their last nine encounters against Scottish opponents.
- The two clubs have met on five previous occasions with Glasgow winning just once - 31-27 at Firhill in January 2002.
- Dylan Hartley, the Saints hooker, has 57 successful lineout throws to his name this season, more than any other player in the tournament.