The Terriers head to Anfield full of confidence after last week's uplifting win against Manchester United and Wagner was keen to play down his first competitive meeting against the godfather to one of his daughters.
Town's unlikely first victory against United since 1952 electrified the John Smith's Stadium and they now bid for their first against Liverpool since 1959.
"It's extraordinary, yes it is, because he's my best friend and he's the manager of Liverpool," Wagner said.
"But I think the real important and extraordinary story is Huddersfield Town meets Liverpool in the Premier League in a competitive game.
"I think nobody should forget this
This is the real extraordinary story
I don't know for how many years, the last time this football club was able to play at Anfield in a competitive game
This is the big story for us
Ramped-up media interest in the Terriers this week has focused on Wagner and Klopp, team-mates and room-mates during their playing days for Mainz in the 1990s.
Wagner was best man at Klopp's wedding and was invited by his friend to take charge of Borussia Dortmund's reserve team in 2011 when he was head coach.
He also reminded Thursday's press conference of the hat-trick he scored as a striker for Gutersloh against Mainz in 1997 when defender Klopp was marking him.
"It's a great relationship
It's more than a friendship," said Wagner
"Maybe he's more a family member rather than a friend
"That's the truth
Now he's Liverpool manager and I'm Huddersfield Town manager and we play in the Premier League on Saturday
"Even when I was in Huddersfield and he was already at Liverpool I never thought we would meet in the Premier League.
"This was never in my head
So now this is the case, for sure it's something extraordinary and this may be another short story around this game on Saturday.
"But as I say, the big story is Huddersfield Town being able to play a competitive Premier League game at Anfield."
Huddersfield's dream start - they beat Crystal Palace and Newcastle in their opening two matches - had been followed by six league games without a win before last week's stunning upset.
"Of course such a result with such a performance gives everybody a boost and confidence for what we have to do in the future," Wagner said
"It helps massively, every single player, and everyone at the club to believe and trust everything we're doing."
The German was reluctant to contemplate the thought that victory at Anfield would lift Huddersfield above Liverpool in the table.
"To show a performance like we did against United is extraordinary," he added
"To do it for two games in a row would be unbelievably extraordinary
We will try."
Source : PA