Griezmann was understood to be on the verge of joining City's local rivals Manchester United during the summer, only to pull out of the deal and commit his future to Atletico after they were hit with a transfer embargo, which expires in January.
Atletico will welcome Diego Costa back into their squad once that ban expires in the New Year, although any Griezmann exit is expected to take place next summer rather than when the transfer window reopens.
Reports in France earlier this week suggested that Barcelona have already agreed a deal in principle to sign the striker, but Sport claims that Man City have now made initial inquiries as to whether Griezmann would be interested in a move to the Premier League leaders.
Griezmann has a release clause of £170m in his contract at Atletico, but Barcelona, Manchester United and City are all said to be willing to spend big in their pursuit of the France international.
The 26-year-old has scored just three goals in his 13 appearances across all competitions for Atletico this season.