But unless 34-year-old Marshall and his Ospreys team-mates can conjure a victory over Guinness Premiership leaders Gloucester, that ambition will effectively die for another season.
The big-spending Ospreys must beat Gloucester - and then topple Bourgoin in France - to have any realistic chance of securing a quarter-final place from Pool Two.
If they progress as one of two best runners-up, the Ospreys could even land a last appointment with Gloucester - but at Kingsholm rather than tomorrow's home venue, the Liberty Stadium.
Scrum-half Marshall said: "The reason I came to the Ospreys was because I thought they had the ambition, drive and squad to win the Heineken Cup - and it is what keeps me going.
"To win the Heineken Cup is what is keeping me in the game at the moment.
"On its day, this team is capable of beating any team - and that is a good feeling.
"We are going to be playing the best team in England - one of the top sides in Europe right now - and if we want to progress in the tournament on big occasions like this, we need to know as a squad we can go out and win these games."
The Ospreys could have Gavin Henson back from a six-week injury absence. But Gloucester are without new England squad member Lesley Vainikolo, who is in New Zealand dealing with family matters.
Saracens host French heavyweights Biarritz on Saturday - when victory would keep them firmly on course for a first quarter-final appearance.
But Biarritz full-back Nicolas Brusque warned: "We consider this game as a quarter-final in itself - and we have prepared accordingly.
"If we lose, I do not think we will qualify. It would be such a blow not to reach the quarter-finals, and our players would take it badly."
Premiership champions Leicester face a Biarritz-style mission on Saturday against Andy Robinson's Edinburgh at Murrayfield, where defeat would bankrupt any hope of catching Pool Six leaders Toulouse.
But London Irish's relentless quarter-final march should continue against injury-hit Pool One opponents Newport Gwent Dragons at the Madejski Stadium, with a probable third bonus-point victory in four starts in the offing.
Bristol head coach Richard Hill, meanwhile, believes his Bristol team will encounter "a different animal" when they target an unlikely Heineken Cup double against French champions Stade Francais tonight.
Bristol head to Paris as Pool Three leaders, knowing that victories over remaining opponents Stade and Cardiff Blues would clinch a quarter-final spot.
But both Stade, who have won their last 15 Heineken Cup home games, and the Blues are waiting to pounce.
With just three points separating the three clubs - it is the tightest group in this season's competition - Bristol, realistically, cannot afford to return home empty-handed.
They beat Stade 17-0 at the Memorial Stadium in November, but their opponents' fortress-type home record suggests a tough task for Bristol.
Head coach Hill said: "With our away record, and Stade's home record, you would put a lot of money on Stade!
"However, confidence is growing in our squad, and at this stage I don't think they are daunted by the prospect of going to Paris.
"The French are a different proposition at home. They don't travel well - but they're a different animal altogether at home."
Cardiff host struggling Harlequins on Friday night, totally in control of their own destiny.
A win against Quins, followed by toppling Bristol away from home on Sunday week, would knock the west-country club and Stade out of contention.
Blues head coach David Young said: "I think this is the first season we've had a realistic opportunity of reaching the last eight for a number of years.
"I think we have shocked a few people that we are in this position."