Manchester United seemed the most likely destination for the world's most expensive player, for whom Madrid paid United £80 million (Dh450.6m) in 2009.
"I know Ronaldo loves Man United and I know he loves the Premier League, but I think he is going to stay," Mourinho said.
"It's just a feeling, no contact, nothing just a feeling."
Even if Madrid received a large offer for the Portugal forward, Mourinho would not expect them to accept.
"What I know is that Real Madrid is such a rich club they don't need to sell," he said.
"It is such a rich club I think they can beat any offer a club can have on Ronaldo."
Mourinho's feeling was backed up by his replacement at the Bernabeu, Carlo Ancelotti.
After Sunday's friendly win at Bournemouth, the Italian manager said: "His future is at Real Madrid, there is no question about this."
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