With City looking set for a trophyless this season, there has been suggestions manager Manuel Pellegrini could be replaced in the summer.
Simeone — who Atletico yesterday confirmed had signed a new contract with them through to 2020 — had been among those mentioned as a potential successor.
And on the latest edition of Sky Sports’ Revista de La Liga programme, Spanish journalist Guillem Balague claimed the Argentinian would be staying on with his current employers despite having had a “huge offer” from City.
However, City sources have categorically denied the club made a bid for Simeone’s services or that they are interested in the 44-year-old.
Since Simeone took charge at Atletico in 2011, the trophies they have won include the Europa League and Primera Division, and they have also reached the Champions League final.
Reflecting on his decision to commit his future to Atletico, Simeone said: “I choose to be here because I am convinced the club will continue to grow,” he said.
“The club keeps growing. I’ve made a decision to stay where I am and decisions are sometimes difficult to make.
“Fortunately I’ve been able to make this decision as I see a club that is moving forward, I see eagerness to grow and people willing to collaborate.”