How could they when standing a lofty and healthy eighth in the latest list of the most valuable club in world football (at €1.24bn)?
And when they boast one of the most overloaded honours lists imaginable? Yet, here they are, off to Kiev later this month and cast in the role of David to Real Madrid’s Goliath.
It seems more ridiculous again given the form of Mohamed Salah, Roberto Firmino, and Sadio Mane and the heavy metal football with which they have silenced Porto, Manchester City and Roma in the knockout stages.
Turn it up to 11 on the Spinal Tap dial just one more time and they won’t be far from a sixth European Cup.
Thing is, we all know this isn’t the full story.
This is the side that been associated for so long with the dodgy goalkeepers and the error-prone centre-backs.
The outfit unable to defend set pieces or tap into any sort of vein of consistency. Even their captain has been identified as a glaring symbol of their relative inadequacies.
You don’t have to go back far to find the latest examples of observers bemoaning Jordan Henderson’s possession of the armband.
Jurgen Klopp has found himself fighting his skipper’s corner more than once since his arrival and not least six months ago after Liverpool let a 3-0 lead slip in Seville.
“Jordan is a proper captain,” Klopp said in the days before Chelsea caught them with an 85th-minute equaliser at Anfield.
He wasn’t when I came in but only because he didn’t know how to do it because nobody had to think about how to be captain at Liverpool because they had one for around 20 years.
Steven Gerrard, the man he replaced, had anointed Henderson as far back as January of 2015 when he told the Liverpool Echo that his then midfield partner had “everything you need to be a great captain”. Many will dispute that, even if Henderson lifts old jug ears aloft in the Ukrainian capital on May 26.
And that’s part of the beauty in all this.
Liverpool are the sweet but spotty teenager who is poised to get the girl. They are the Arcade Fire of football, a hodgepodge of weird musical instruments — glockenspiels and synthesisers and double bass — that looks like a recipe for disaster on paper but somehow comes together to produce a string of cracking, catchy tunes.
The Champions League has long usurped anything international football can offer in terms of standard so the prospect of such a clearly imperfect Liverpool side edging so close to the game’s ultimate prize is strangely satisfying.
It’s not that we haven’t known such flawed talents as Henderson before. Run a finger through the vast majority of sides to claim European primacy and it soon becomes clear that Djimi Traoré isn’t the only man who could be deemed fortunate to have a winner’s medal to his name. For all his faults, Traoré did at least play his part on the night.
Josemi, Antonio Nunez, and Igor Biscan all have Champions League winners’ medals in their possession and none of them featured in Istanbul 13 years ago.
Ditto the likes of Jonathan Greening who was unused by Manchester United in 1999 and ended his playing days only last year with Tadcaster Albion in the Northern Premier League.
Bob Bolder went on to play over 300 games for Charlton Athletic but he was back-up goalkeeper to Bruce Grobbelaar when Liverpool went all the way in 1984.
Having to sit and watch as his Zimbabwean teammate spooked the Italians with his jelly legs didn’t exactly dilute his sense of personal satisfaction.
“It always pops into the conversation now and again and if one or two people get above themselves I will bring out my European Cup medal,” Bolder, who never featured in a competitive game for the club, told Liverpool’s website four years ago.
“It’s nice for me to have that as not many people can say they have one.”
The difference with this Liverpool side is that they have come this far with so many characters who might normally be understudies having assumed such central roles in the unfolding drama - and the likes of Lloris Karius and Dejan Lovren offer nothing if not the tantalising prospect of drama.
Liverpool have a raw 19-year old kid in Trent Alexander-Arnold at right-back, a holding midfielder in Henderson whose worth as a player and a leader has so often been questioned and, alongside him, another honest grafter in James Milner who has been stubbornness personified in working a groove for himself in Jurgen Klopp’s thoughts.
None of those names would trip off the tongue if you were Pep Guardiola or Jose Mourinho and your bosses were dropping blank cheques on your desk. It’s that fact, as much as Salah’s brilliance and the webs woven by the Egyptian, Firmino and Mané, that has made this chapter in Champions League history so beguiling.
Theirs would be the perfect imperfect success.