The Slovenia international has grown to be one of Europe's best shot-stoppers since succeeding Thibaut Courtois and City, whose leaky defence is the cause of much recent concern, have taken notice.
Pep Guardiola's side have conceded 26 goals in the Premier League so far this season, with summer signing Claudio Bravo coming in for renewed criticism in the wake of their 4-0 loss to Everton.
Oblak, who is out injured until the end of February, has interested several English clubs. Arsenal, Chelsea and Manchester United are all also said to have made early contact about his availability but City's interest is strongest.
Atletico, however, have no desire to sell and are pointing any suitors to the keeper's €100 million (£86.7m) release clause, as they did when they successfully fended off interest in star forward Antoine Griezmann last summer.Los Rojiblancos have only let in 14 goals in La Liga this season, the second-best defensive record in the Spanish top flight behind Villarreal's 12, while Oblak has only conceded twice in six Champions League outings.