Manchester United are reported to have agreed personal terms with the Atletico Madrid star and are willing to pay his £85million release clause in the summer.
But earlier today United denied reports that an agreement had been reached with Griezmann.
How Man United could look with Antoine Griezmann
Wed, February 1, 2017
Is this how Manchester United's squad could look with Antoine Griezmann
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Is this how Manchester United could look with Antoine Griezmann
And, according to Spanish newspaper Marca, the Portuguese coach is unsure whether Griezmann will adapt to his philosophy.
It is claimed that senior figures at United are pushing for the deal to happen despite Mourinho's reservations.
Manchester United boss Jose Mourinho is not convinced by Antoine Griezmann
The report adds that with Atletico's ongoing transfer ban they would be committing a ‘sports suicide’ by selling Griezmann without being able to bring in a replacement.
Apart from Zlatan Ibrahimovic, United's forwards have struggled to regularly score goals this season.
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Antoine Griezmann is one of Europe's best strikers
The 35-year-old has scored 19 in all competitions while midfielders Paul Pogba and Juan Mata are joint next best on seven.
Marcus Rashford and Anthony Martial have six each while captain Wayne Rooney has just five for the season.