Griezmann, 28, has been one of the most prolific strikers in Europe over the last five years, scoring 133 goals in 257 appearances for Spanish club Atletico.
The World Cup winner continues to be linked with a summer move and Manchester United have held interest in the 28-year-old for a number of years.
The Daily Star even say Premier League giants United have prepared a £95million offer for Griezmann, who netted 21 goals in La Liga last season.
Griezmann is expected to sign a deal with Barcelona on July 1, however, and it is claimed the striker is desperate to join the club to play alongside his hero Lionel Messi.
Frenchman Griezmann is said to have spoken to Messi last year ahead of a proposed move to Barcelona but the deal fell through.
Speaking to reporters last week, Griezmann appeared to give Manchester United hope of a deal by suggesting he could leave Spain altogether during this summer transfer window.
Theres a need for patience, as its still soon, Griezmann said after Frances 4-0 win against Andorra.