According to the French media, Atletico Madrid star has already struck a deal with Premier League giants Manchester United.
Griezmann has been the subject of transfer rumours linking him with a move away from the Vicente Calderon.
The French star has enjoyed success with France and Atletico in the recent years.
Canal Plus has reported that Griezmann has agreed to join Manchester United at the end of the season. Man United will play Griezmann’s £85m release clause to acquire his services.
This will make him their second high profile signing in recent history with Paul Pogba also making an £89m move from Juventus to Manchester United.
Pogba and Griezmann’s close relationship has also added fuel to the speculation.
“I always ask Paul Pogba about Manchester United,” said Griezmann.
“I think they are a huge club with a really good infrastructure.
“I ask Paul about some of the players, and if they’re really that good, or if Jose Mourinho is really that good.”