As Real prepared for Wednesday's Champions League round-of-16 second leg against CSKA Moscow at the Bernabeu, Mourinho and Ronaldo appeared together at a news conference and both were quizzed about the Chelsea reports.
"He is going to continue," Ronaldo, who netted Real's goal in last month's 1-1 first-leg draw in Moscow, said with a smile. "He is going to continue with us."
Mourinho responded with a terse "No" when asked if his future depended on Real winning Europe's elite club competition, as the La Liga leaders chase a 10th European crown and their first since 2002.
Responding to a question about Wednesday's game, he added: "If my future depends on the result of this tie? No. Unless the club decides to fire me, but I do not base my decisions on winning or losing one match."
The most successful manager in Chelsea's history, Mourinho left in 2007 after falling out with the club's ruthless billionaire owner Roman Abramovich.
He remains hugely popular with the Premier League side's fans but after this season has two more years to run on his four-year contract with Real, with whom he has won a King's Cup since joining from Inter Milan in 2010.
Mourinho and Ronaldo were asked about Lionel Messi's goal haul against Bayer Leverkusen last week, when the Argentine World Player of the Year became the first player to score five in a Champions League match.
"Very good, happy for him and for football," said Ronaldo, who was World Player in 2008 before Messi won the award three times in a row.
"I don't know if I would be able to do it one day but I hope I can," added the former Manchester United forward.
The prolific pair have again been conducting a personal scoring duel this season and Ronaldo has 32 goals in La Liga, two more than Messi, and 40 in all competitions, compared with 50 for the Barca forward.
"I don't care what the others do. I just focus on myself and my team," Ronaldo said. "If I score, good, if not it doesn't matter. I am relaxed about it."
Mourinho said of Messi: "Scoring five goals is never easy in any competition. It was a very good night for him."
