The Terriers head to Anfield full of confidence after last week's uplifting 2-1 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.