The 42-year-old became arch rivals with the Portuguese between 2010 and 2012 as the Blaugrana fought out numerous heated battles with their old foes following the Portuguese coach's arrival in the Spanish capital.
And Klopp is looking for a similar fierce rivalry with the future Bayern boss, only without the bad blood.
"I want to become Guardiola's new Mourinho. We want to be an unpleasant opponent for Bayern in the next few years," Klopp told Sport Bild. "If Pep Guardiola doesn't like me during the game or because of the result, that's not a problem."
He added, "I do not believe that Pep has bad feelings toward his rivals, though. I think that I will get along very well with Pep. I have a good relationship with Mourinho as well."
Guardiola recently signed a three-year deal with Bayern, starting at the end of this season.