With City looking set to go trophyless this season, there has been plenty of talk of late about the prospect of manager Manuel Pellegrini being replaced in the summer.
Simeone - who Atletico on Tuesday 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 to Press Association Sport that 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.
Chilean Pellegrini guided City to the Barclays Premier League title, victory in the Capital One Cup final and the club's first-ever participation in the Champions League knock-out rounds last season, his first term in the job.
Since then they have suffered a second successive last-16 exit in the continental competition, and in the Premier League - their last hope of silverware in 2014-15 - they are currently second, six points behind Chelsea, who have a game in hand.
Source : PA
Source: PA