Mourinho is preparing for a second spell in charge of Chelsea after making a return to the Premier League, with speculation rife that Ronaldo would follow suit.
Manchester United seemed the most likely destination for the 28-year-old but Mourinho thinks that, even if Real receive a large offer for the Portuguese forward, he would not expect them to accept.
"I know Ronaldo loves Man United and I know he loves the Premier League, but I think he is going to stay," said Mourinho.
"It's just a feeling, no contact, nothing, just a feeling.
"What I know is that Real Madrid is such a rich club they don't need to sell.
"It is such a rich club I think they can beat any offer a club can have on Ronaldo."
Real coach Carlo Ancelotti backed up Mourinho's thoughts following his side's win at Bournemouth on Sunday.
Ancelotti added: "His future is at Real Madrid, there is no question about this."