The two were team mates at Mainz in the 90s and Wagner coached the second team at Borussia Dortmund when Klopp was in charge of the senior side.
They will face each other from opposing ends of the dugout for the first time this weekend.
"It's extraordinary because he's my best friend and manager of Liverpool but the real important and extraordinary story is Huddersfield Town beats Liverpool in the Premier League in a competitive game," Wagner told a news conference on Thursday.
"For sure I'm looking forward to it... even when I joined Huddersfield and he was already manager of Liverpool I never thought we would meet in the Premier League."
Wagner said his team, who are 11th in the table with 12 points and one behind ninth-placed Liverpool, were brimming with confidence after the United game.
"Of course such a result, with such a performance, gives everybody a boost and the confidence for what we have to do in the future. It helps massively to grow the belief in what we are doing. I'm sure this will help us for the weekend," he said.
"If we are able to play a game like last week when we did not make one mistake... then I think it depends on how Liverpool will react."
Stuttering Liverpool, who lost 4-1 to Tottenham Hotspur last week, have let in 16 goals so in their worst defensive start to a league season since 1964.
Huddersfield winger Collin Quaner is fit again after recovering from a calf strain.
(Reporting by Shrivathsa Sridhar in Bengaluru, editing by Ed Osmond)
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