Reports in Spain suggested City were ready to meet Atleti's €150 million (£136m/$170m) release clause for Saul, as they search for a long-term successor to Fernandinho.
Ex-Barcelona boss Guardiola spoke of his admiration for Saul at a news conference ahead of City's Champions League match against Hoffenheim, but insisted the 24-year-old's long-term future is at the Wanda Metropolitano.
"Manchester City have interest in 125 players in the last day, so one more," he said in an initially weary response to the rumour.
"Sometimes I read 'Pep Guardiola is interested in this player'. Still I didn't know him.
"[Saul] is a fantastic player but we are not interested in him. He is an Atletico Madrid player who is going to stay there for a long time because he is an exceptional player."
One midfielder set to feature prominently in City's long-term future is Phil Foden, after the England Under-21 international signed a contract extension until 2024 with the Premier League champions.
Securing a new deal for Foden is a coup for City after his former youth-team colleague Jadon Sancho's departure to Borussia Dortmund last year, while fellow teenager Brahim Diaz is reportedly set to reject an extended stay in favour of a switch to Real Madrid.
"I'm delighted, I'm happy. It would have been our desire for Jadon to stay here, Brahim to stay here. That was our wish," Guardiola said.
"With Phil, we convinced him because we believe he has something unique, a special player like Jadon and Brahim.
"In the next five or six years we are going to help him to be a better player and he is going to help us to be a better team.
"He is an incredible fighter and he is a Manchester City fan."