Mourinho's spokesman Eladio Parames was reported to have said the Portuguese coach was considering his future due to a lack of support from the club, but the former Chelsea manager decided to put the record straight himself.
"Only those who don't know me can dream, make up or believe I may leave Real Madrid at this stage," Mourinho said in a statement on the club website.
"I believe many people were surprised by the quality of the football showcased by Real Madrid during the pre-season and it would be surprising news to them if I left the club now. Impossible!.
"I have a fantastic President who is very intelligent and with whom I have a great friendship.
"I also have a Director General who works for the club 24 hours a day, so my motivation is enormous and my 'Madridismo' is even greater than that of some pseudo-Madridistas... there is no way I'm leaving. No way!"
Mourinho has been in the headlines since last Wednesday's Spanish Super Cup defeat by Barcelona at the Nou Camp, when television cameras caught him poking Barca's assistant coach Tito Vilanova in the eye.
That incident, in the middle of a mass confrontation between players from both teams at the end of the match, soured what had been an enthralling game, and has further fanned the bitter rivalry between the two clubs.
Mourinho and Vilanova are to be investigated over the eye-poking incident, the Spanish federation said earlier on Tuesday.
"I also wish to apologise to Madridistas, and only to them, for my attitude in our last game," Mourinho added.
"Some people are better adapted to the hypocrisy in football than I am, and they hide their faces and speak in whispers deep inside tunnels.
"I'm not learning to be a hypocrite and I don't want to be one."
Real's next match is a friendly at home to Galatasaray on Wednesday.
