Lampard accused Klopp's coaching staff of crossing a line and showing a lack of respect by leaping up, shouting and smirking at him during Chelsea's 5-3 defeat at Anfield earlier this summer.
But Klopp insists there is no lasting issue between the two managers and that he didn't mean to spark tensions when discussing Chelsea's exorbitant transfer spending this summer earlier this month.
"There is no rivalry," Klopp said ahead of his side's trip to Stamford Bridge.
"You all make a story about me saying something on the transfer behaviour of Chelsea. What I said was in the situation we are in we cannot deal with the situation like other clubs, one of them was Chelsea.
"Then you create a rivalry between Frank Lampard and me. Why? We meet two times a season. I respect a lot what he is doing. He is probably a really nice guy but I don't know him in private like he doesn't know me in private.
"On the sideline we are quite animated and emotional and sometimes we say a few words which a few minutes later we wish we didn't say.
"That's how life is. That's how football is. It's nothing more than that. I have no problem at all with Frank Lampard."
Klopp acknowledges it will be a tough ask to leave west London with three points and admits his side have some things to work on following their game against Marcelo Bielsa's side.
"We played Chelsea pretty often last season and it was always difficult. Their game against Brighton was tough," the German added.
"We have no idea who Frank will play with so many options.
"We have to focus on ourselves and we've got enough work to do on that.
"There were a lot of things that were good in the first game, others weren't.
"Now we have to make sure we can transform out training onto the pitch. we have to be at our best otherwise it'll be tricky."