The two have exchanged words in public over the past year, while there was a heated exchange during a recent Premier League encounter at Anfield.
The 'rivalry' came to the fore once again this week when Klopp said Liverpool weren't able to spend money on players like Chelsea, which Lampard found 'amusing'.
However, Klopp says people should stop paying attention to the gossip when it comes to these incidents.
"There is no rivalry," he said, as per the Mirror.
"You should stop reading newspapers! When I heard what all the different journalists made up, I really don't get that.
"When you ask me a question, I answer it and everybody takes it the way they want to take it. It might be a language issue or something.
"You made up a story that I said about the 'transfer behaviour of Chelsea'.
"What I said was in the situation we are in, we cannot deal with the situation the same as other clubs. One of them was Chelsea.
"Then you create a rivalry between Frank Lampard and me. Why? We meet two or three times a year.
"I respect a lot what he's doing. He's probably a really nice guy, but I don't know because I don't know him privately and he doesn't know me."
