"In Italy they have insisted that I'm going to return, but it isn't true," the 34-year-old centre-half told Marca.
"I've always said that I've been happy at Real Madrid and in Spain and I'm glad I signed for this team. No one from the club has said that there is an offer for me; nor have they said they want to sell me. I'm sure I'll remain at Real."
Cannavaro signed for Madrid from Juventus after leading Italy to victory in the World Cup last year, but had a difficult first season with the Liga side.
La Liga
Drenthe keen to make Madrid move
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After the sacking of coach Fabio Capello - who Cannavaro also played under at Juve - and signing of two centre-backs Christoph Metzelder and Pepe in the close season, there has been speculation that Cannavaro might return to the Old Lady.
But Cannavaro said that although he was grateful to Capello, his future in the Spanish capital had not been dependent on the presence of the Italian.
"I've worked with Capello for three years and I've learned a lot from him," he continued. "He made me into a winner and I'm thankful to him for that.
"But I signed a three-year contract with Real Madrid and not with Capello."
The defender admitted to having problems in his first season in Spain, but was confident he would recover the form he showed at Juventus in the forthcoming campaign.
"It was to be expected that after winning the World Cup and coming to a new country I would suffer and have problems," he said.
"But I've rested up well over the summer, I'm now familiar with Spanish football and I hope to perform at a higher level.
"My aim is to help the team with the Champions League - that is the only trophy I have left to win."