It had been claimed in the German media that Klopp had admitted that he had been informed by the Real Madrid coach that he was to leave Spain at the end of the ongoing season to take charge of the Premier League outfit.
However, Klopp has denied the report, which he has described as "a made up story" by the press.
"It is an absolutely ridiculous story. I never told anyone that Mourinho is going to Chelsea or another club. I'm not a person who does things like that," he told reporters.
"I heard this story before our game with Fortuna [Dusseldorf] and I have to admit I was very sad and angry because it is completely false.
"It is a made up story. Mourinho is a colleague and a friend and I would never mess around in such a manner."
Klopp's Dortmund will face Mourinho's Madrid in Spain in the Champions League tomorrow night.