Atletico Madrid’s star hitman admitted earlier this week he is ready to leave in the summer.
And Manchester United are frontrunners to sign the France international, who has an £86million buyout clause.
Griezmann is intent on winning trophies and Jose Mourinho wants to bring him to Old Trafford to strengthen his frontline.
Qualification is now secured for the Champions League too after last night’s 2-0 Europa League triumph over Ajax in Sweden.
And that was believed to be key to Griezmann’s decision over his future, which he wants sorted across the next two to three weeks.
Zinedine Zidane was unwilling to let Karim Benzema go to welcome Antoine Griezmann to Real Madrid
However, while he appears willing to join Manchester United, having outlined on Monday there was a 6/10 chance of him signing, Old Trafford is not his No1 choice.
Journalist Josep Pedrerol told Spanish show El Chiringuito that the 26-year-old’s priority was to secure a move to Atletico’s neighbours and direct rivals.
Zidane has not made big efforts to bring Griezmann to the Bernabeu, though, and offer him a chance to stay in La Liga.
Instead, the striker now looks set to leave Spain for England.
Pedrerol said: "Griezmann is pissed because Real Madrid has not taken the step.
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Antoine Griezmann's first choice for a move is apparently Real Madrid over Manchester United
[Griezmann] was confident that Real Madrid would take the step
“There is zero chance of working under Zidane.
“He was confident that Real Madrid would take the step."
“[Griezmann] is telling Zidane he has failed him."
Spanish outlet Don Balon add Zidane did ask Madrid president Florentino Perez for Griezmann.
But buying the Atletico star would have apparently required selling Karim Benzema, which Zidane was not willing to accept.