The 45-year-old trainer has refuted claims made in the German media that he suggested the Real Madrid coach is Chelsea-bound in the summer
According to the outlet, the 45-year-old coach revealed Mourinho would quit Real Madrid this summer in favour of former club Chelsea.
However, Klopp has rubbished the reports, insisting he is infuriated about what has been written and said that the Portuguese trainer is a friend of his whom he would not reveal such things about.
"It is an absolutely ridiculous story," he told reporters. "I never told anyone that Mourinho is going to Chelsea or another club. I'm not a person who does things like that.
"I heard this story before our game with Fortuna 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 will come face-to-face with Mourinho on Tuesday as his Dortmund team travel to the Spanish capital for the second leg of their Champions League semi-final.
Die Schwarzgelben hold a 4-1 lead from the first leg at Signal Iduna Park, where Robert Lewandowski scored all the hosts' goals with Cristiano Ronaldo grabbing the Blancos' away goal.