The Atletico Madrid striker has been in poor form this season, scoring just twice in La Liga so far.
Le 10 Sport further reports that Griezmann's transfer can happen due to a clause in his contract.
Griezmann has been consistently linked to Manchester United for the last two or three years, and looked all-but-certain to come to Old Trafford last summer.
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When asked whether he spoke to United boss Mourinho - who is a huge admirer of the France international - on the phone regularly, Griezmann answered: 'No'.
A January transfer is unlikely, despite Diego Costa finally becoming eligible for Atletico when the transfer window reopens, with a summer switch more plausible.
City have also made a "substantial offer" for PSG midfielder Claudio Gomes, with L'Equipe claiming that the player has yet to respond.
But with the 26-year-old's release clause lowering to £87million on 1, July 2018, Barcelona have opened talks ahead of a potential mega summer transfer.
West Ham are putting into place plans to make David Moyes' first signing since replacing Slaven Bilic as manager at the London Stadium. He will also present to be a viable long-term replacement for the aging Luis Suarez. He developed in Real Sociedad's youth system, having grown up near the border to Spain.
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