Their impressive victory comes a week after rivals Manchester United beat Paris St-Germain by the same scoreline in France to seal Ole Gunnar Solskjaer’s best result since taking charge of the club.
And fans now think a mega showdown between the two clubs is on the cards in Friday’s Champions League quarter-final draw.
“Wow What a time for UEFA to make money. They will simply draw Liverpool v Man United. Don’t say I didn’t say so,” wrote one fan on Twitter.
“Liverpool vs Man United quarter final,” wrote another.
“Surly 2 English team will play against each other now in the QF. Liverpool vs Man United will be a cracker,” added another.
A fourth was excited about the prospect: “Liverpool vs Man United next round would be a dream.”
“Na Liverpool vs Man United incoming,” tweeted another fan.
The conspiracy theory about Man Utd playing Liverpool comes as
United and Liverpool played each other in the Europa League during Klopp’s first season in charge.
And his Reds side got the better of Louis van Gaal’s Red Devils on route to defeat against Sevilla in the 2016 Europa League final.
Liverpool beat United 3-1 earlier this season in what turned out to be Jose Mourinho’s last match in charge.
But Solskjaer fared better last month when United held Liverpool to a dull 0-0 draw at Old Trafford.
When quizzed about the win over Bayern, Klopp said: “In a game like this you can never rest. It is absolutely deserved. It is so difficult to play here away at Bayern Munich.
“The first goal, I will want to watch it back like 1,000 times! Defensively it was so good. We didn’t defend the way we do usually in the away games of the Champions League but today we did.
“Virgil van Dijk gives organisation on set-pieces and he is dangerous. He is a massive threat. The size we have and the power we have… it was a big goal.
“In a game like this, there will be mistakes but you have to stay in the game. Control the moments you can control and stay in the game. The game didn’t look like Bayern ever outplayed us.”