According to The Sun, the Citizens would be willing to send their all-time goalscorer to Atletico Madrid to help Griezmann move to the Etihad.
The French striker is a primary target of City boss Pep Guardiola and has an £85m release clause.
A source from The Sun said: "Atletico have contacted Sergio's representatives to see if there is any chance of getting him back.
"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."
Barcelona have also made their interest in Griezmann known.