It was reported in the Spanish press at the weekend that the Portuguese would leave the Bernabeu in June, with an alleged training-field bust-up between Spain defender Sergio Ramos and Mourinho - news of which apparently leaked from within the camp - also adding fuel to the fire of disharmony in the squad.
However, Mourinho brushed aside talk of problems ahead of the crucial cup game against rivals Barca in which they will have a 2-1 deficit to overturn.
"I do not provoke cliques," Mourinho told www.as.com. "I know nothing about the leaks. I feel very supported by the board, we're currently in the midst of a very good spell."
Real received a much-needed boost when the Spanish football association announced it was not going to take any action over Pepe's alleged stamp on the hand of Barcelona's Lionel Messi during a fiery first leg.
The defender was branded "shameful" and "embarrassing" in the Spanish press following the incident although he insisted it was unintentional.
And Mourinho was keen to focus on the progress that has been made at the club since he took charge in 2010.
"My team has a chance to try and play," he said. "We realise that we lost against the team we are playing and that we can go out of the Copa del Rey.
"In the league we...have taken a five-point advantage over the team which everyone thinks is the best team in the world.
"That's because we are not doing as bad and we do not have as many problems as people think.
"When I came here the club had a tradition of being eliminated from the Copa del Rey by teams from the lower divisions.
"When I arrived, we were not seeded in the Champions League and now we have the record for most wins in the group stage. I seem to have so many problems.
"This game does not mark a 'before and after' in my career."
In the other quarter-finals, Espanyol travel to Mirandes on Tuesday night with a 3-2 goal advantage, Mallorca will look to overturn Athletic Bilbao's 2-0 lead on Wednesday and Levante trail Valencia 4-1 ahead of the return leg on Thursday.