Atletico coach Diego Simeone has not denied that his side were interested in Cazorla saying "anything is possible."
But Cazorla, who joined Arsenal from Malaga in a £15m deal last summer, played down the claims, insisting he is happy at the Emirates.
He said: "There has been a lot of speculation about a move to Atletico Madrid but I'm very happy at Arsenal, I have a contract there and I start training on Monday.
"Perhaps I will return to Spain one day, but right now it's very unlikely."
Atletico have been busy in the transfer market this summer, signing David Villa from Barcelona and Leo Baptistao from Rayo Vallecano.
Although Cazorla stressed he was not about to link up with his Spain team-mate Villa at the Calderon, he said he was pleased for him.
"I'm very happy for Villa, because he had a difficult year with Barcelona due to his injury (a broken leg he suffered in December 2011), but now he's got another chance to shine again," he said.
And Cazorla admitted this would be a big season for him personally, with the World Cup on the horizon. He missed Spain's victorious campaign in South Africa in 2010 because of a back injury.
He said: "I still have unfinished business in the World Cup after missing the last one because of my back.
"I really want to experience a World Cup, so I have to have a great year with Arsenal. I hope this year is even better than the last."