Gloucester, two points clear of the Ospreys and with a home match against Ulster Rugby to come on Sunday, remain favourites for the Pool honours but a debut Ospreys win in France at the sixth attempt when they clash with Bourgoin at Stade Pierre Rajon would put them on a minimum 21 points.
The Ospreys have gone down to defeats on their previous five trips to France, against Stade Français Paris (twice), Toulouse, Castres Olympique and ASM Clermont Auvergne.
"All we have to do is go to France and win a game of rugby," said Coach Lyn Jones. "It sounds really easy - but in practice it is very, very difficult.
"I have coached a team who have won once in France - Neath at, of all places, Bourgoin - and if you want to do well in this tournament you have to go to France and win.
"It is really quite simple, we have to go there and win and it would be fantastic for Welsh rugby if Cardiff Blues and ourselves could both qualify. It is all there to play for and that is the beauty of the Heineken Cup, it is right on a knife edge from start to finish.
"We don't know if a win in Bourgoin will put us through but it should put us in pole position as a best qualifier.
"I was delighted with the performance against Gloucester and after beating Ulster in Round 3 we knew we needed three victories to take us to 21 points. Because of the dream start Gloucester had in this tournament it has meant they have pulled too far away for anyone to catch them so we have to try and come through as a best qualifier."
Former All Blacks scrum half Justin Marshall was the Heineken man-of-the-match against Gloucester and added: "There is no worse position to be in than to have other teams controlling your destiny and we have to go out to France and win.
"Our forwards were outstanding against Gloucester, they competed everywhere and got us going forward - which makes the scrum half's job so much easier when you are playing off the front foot against a very good side.
"If they front up like that again next week then we are a pretty good side."