All Barcelona attempts to prise the Brazilian playmaker away from Merseyside are doomed to failure, according to those in charge at Anfield.
On this evidence, Coutinho might struggle to win back a place in Liverpool’s forward line.
Progression to the Champions League group stages, for only the second time in eight seasons, was secured comfortably.
Or at least, as comfortably as it could have been, given their defensive wobbles.
Make no mistake about it, Liverpool look awesome going forward.
Better teams than Hoffenheim, though, could enjoy a field day against their back line.
It seemed as if Klopp was on a mission to prove a point to Hoffenheim midfielder Kerem Demirbay, who had cheekily claimed his team played better football.
The home side’s response was to score three times in the first 21 minutes. Indeed, as Emre Can volleyed in Roberto Firmino’s cross for that third goal, ending a sumptuous move begun by a Sadio Mane backheel, Klopp could be seen shouting: “That’s football.”
It was a breathless start. In the first three minutes, Mo Salah headed over at the far post after a Trent Alexander-Arnold free-kick had been blocked, and Mane was denied by the trailing leg of keeper Oliver Baumann after he was played in.
The first goal was not long in following, and it came courtesy of a sublime build-up and a touch of fortune.
Firmino’s ball opened up the Hoffenheim defence for Mane to run clear, and this time Mane checked before backheeling into the path of Can, whose shot beat Baumann after a slight deflection.
Liverpool’s second goal came soon afterwards. This time Firmino, in space on the left, cut a low ball back for Georginio Wijnaldum to roll a shot against the post, before an unattended Salah whacked in the rebound.
As Can volleyed in No3, Hoffenheim boss Julian Nagelsmann knew he had to do something.
The decision to play former West Ham midfielder Havard Nordtveit in a back three had been a bad error of judgment. With just 24 minutes gone, Nagelsmann put Nordtveit out of his misery and sent on Mark Uth in attack.
The change unsettled Liverpool.
Serge Gnabry, once of Arsenal, dinked wide a great chance to pull one back for Hoffenheim, before Uth had more success, taking on Sandro Wagner’s pass and cutting a shot across Simon Mignolet and into the far corner of the net.
That was a sobering moment for Liverpool. They still almost added a fourth before half-time, with Firmino denied by Baumann’s block, before Mane steered an effort wide.
But then they almost conceded a second as Gnabry whipped a shot just wide from out on the left.
The German side did not look a great deal more comfortable defensively after the interval, even after Nordtveit’s exit, and Wijnaldum was unlucky not to score when he strode through and lifted a shot over via a touch by Baumann.
He then beat away a Mane effort and made a further save from Wijnaldum.
Baumann’s brilliance was not matched by those in front of him. Vogt’s feeble touch allowed Jordan Henderson to dispossess him and run clear before rolling the ball across for Firmino to tap in No4.
Not that Liverpool’s habit of conceding soft goals had completely gone away.
With 11 minutes to go, they were caught out, with Dejan Lovren somehow left marking two opponents as former Leicester forward Andrej Kramaric’s crossed from the left, and Wagner headed in.
