The Argentine international arrived at the Etihad from Atletcio in 2011. Earlier this season, he became City's leading goalscorer and is on course to win his third league title with the Manchester-based club.
According to The Sun, Pep Guardiola has set his sights on signing Griezmann after the end of the 2017/18 season to bolster his side's attack. He has a release clause of €200m (£174.2m, $248.7m) in his contract, which will be lowered to €100m (£87.1m, 124.3m) on 1 July.
Diego Simeone is looking at the option of bringing Aguero back to Atletico. They have already made enquiries with his representatives to find out if there is any possibility of re-signing the striker.
The Rojiblancos want Aguero to link up with Diego Coast to lead Atletico's attack. The Brazil-born Spain international returned to Wanda Metropolitano from Chelsea last summer and are now targeting re-signing another former player.
Guardiola is not looking to sanction fan favourite Aguero's sale in the summer transfer window. However, the idea of signing Griezmann as part of the deal could be tempting for the Catalan manager. City will demand £60m from Atletico for Aguero.
"Atletico have contacted Sergio's representatives to see if there is any chance of getting him back," a source was quoted as saying by The Sun.
"Pep doesn't want him to go, but has been looking at bringing in Antoine Griezmann, so there could be something there. Pep is a massive fan of him and his clause at the end of the season is a bargain for a player of his quality.
"City have made discreet enquiries over Griezmann in the past, so there is the interest from both sides."
Any approach from City to sign Griezmann will see them face competition from Barcelona. Guardiola's former club are also interested in signing the former Real Sociedad star. There were reports the La Liga leaders had agreed a deal with the forward, which was denied by Ernesto Valverde's side.
It should be seen whether City will be able to beat Barcelona in signing Griezmann. Should they fail to do so, will they still allow Aguero to leave the club in the next summer transfer window.