There is no denying that it's not looking good for them at this stage. They not only need to accumulate 10 points – two bonus-point wins – from their remaining two pool games, but also need results in other pools to go their way.
It's a big ask, especially for a side which has managed to score just three tries in their previous four European outings. For a team of such renown, it's a paltry return. But they do have a chance, no matter how slim.
Sometimes that's all a team of Leinster's capabilities need. What others might see as an impossible feat, they see as a challenge. And they will be hugely enthused by the return of so many important players in recent days, as well as those scheduled to return this week.
On Friday night, Brian O'Driscoll unfurled his cape, perhaps for his last European adventure, to answer the call to arms. He was joined by Rob Kearney and Luke Fitzgerald. And with Isa Nacewa and Richardt Strauss due back this week, there is a healthy glow to Leinster.
Their season is salvageable. But they must win their remaining two games with bonus points. With the utmost of respect to Scarlets, achieving that shouldn't be too problematic in the RDS on Saturday night.
Replicating the feat against Exeter in Sandy Park Stadium a week later will be infinitely more difficult.
Exeter really made Leinster sweat in the corresponding fixture in the RDS at the start of the European season. The home side just about came out on the right end of a 9-6 scoreline, thanks to the accuracy of Jonathan Sexton from the kicking tee.
Leinster's team will, injuries permitting, be at its strongest for these next two weekends and even though their ambitions are teetering precariously above an abyss, past achievements make it a folly to bet against them.
Leinster have reached a blissful state beyond self-doubt. Theirs is a squad liberally sprinkled with star dust but grounded in a professional ethic.
Clermont are through to a home quarter-final with 18 points already in the bag. They should defeat Exeter at home and encounter few problems in accounting for Scarlets, even allowing for the loss of Aurelien Rougerie for those games. The only real question about Clermont's game is whether or not they will win with bonus points in both games.
But despite the huge task facing Leinster, they are in the best shape of the season. They have only three tries scored in their four European games so far but the potential to open up on teams is very real.
Exeter took a beating from Northampton at the weekend and their confidence won't be improved following their trip to France this weekend.
In contrast, Leinster should be able to manufacture a four-try win over Scarlets this weekend, which would leave them in a good position to chase a similar victory at Sandy Park. And with a sniff of redemption in their nostrils, they can be expected to finish their pool with 20 points.
That total is the best Leinster can hope to achieve but it would still leave them needing results elsewhere to go their way.
In Pool 1, Munster, despite being in third position, are in a stronger position. They play Edinburgh away this weekend and finish the pool stage of their season at home to Racing Metro, who are in second place with 12 points (one ahead of Munster).
Munster will need five points from at least one of their remaining games and they will aim to accomplish that this weekend.
Edinburgh are fighting for pride at this stage but they are a shadow of the side that looked so irresistible when reaching the semi-finals of the competition last season. The Braveheart element that was so successful last season has been diluted with the addition of journeymen to the roster and their form and results have suffered as a consequence.
It wasn't in Munster's plan to lose so abjectly to Cardiff on Saturday night but they should be able to bounce back and get the job done in Scotland, which would leave them in a strong position heading into the final round of matches.
A second bonus-point win would see Munster finish on 21 points and guarantee them one of the two runners-up spots. It's in their hands, which makes it a very strong possibility.
In Pool 4, Ulster's loss to Northampton in Ravenhill has complicated matters. Had they beaten the Premiership side back-to-back, they would be home and hosed at this juncture. As things stand, they are still in control with a three-point lead over Castres.
They will beat Glasgow at home this weekend but if Castres can defeat Northampton in Franklin's Gardens it will make for a very nervy final game between the two sides in Stade Pierre Antoine.
Connacht are away to Harlequins this weekend but it is the final home game against Zebre they will be targeting. They have two wins in the competition so far and will want to finish on a high to give Eric Elwood a fitting send-off for his last European game.
Of course, the ongoing speculation about who will eventually succeed Elwood is counter-productive for Connacht.
It is hard for players to motivate themselves when they know they are playing for a boss who is leaving and they are reading and hearing about numerous candidates ruling themselves out for the post, turning it down or being overlooked altogether.
Their big win over the Dragons at the weekend will help with their preparations and they are hugely fortunate that they have Zebre in their last game – although with the Italian side improving with every game, sometimes it's best to be careful what you wish for.