Bild speculated last week that Mourinho has told Klopp that he will be leaving Los Blancos come the summer.
However, Klopp looked to deny this over the weekend.
“It's a ridiculous story. I never told anyone that Mourinho is going to go to Chelsea or another club,” he told reporters.
“I'm not a person who does things like that. I heard this story before the game against Fortuna and I have to admit that I felt very sad and angry, because it is completely false, a made up story.
“Mourinho is a colleague, a friend, and it would never occur to me to mess around in such a manner.”
Klopp was also cornered over the weekend by AS for comment on the Champions League semi-final, which has the Germans heading out to the Spanish capital with a 4-1 advantage.
“No-one said that this was done and that we were in the final.
“It is normal that Madrid will believe with their fans behind them. I will try to do the same with my players. There is a long time until the final. The problem is that we all want to be in it.”
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