Griezmann has been linked with Manchester United, Barcelona and Real Madrid last season but he decided to remain in the Madrid capital due to FIFA ban on Atletico Madrid which prevented the club from making any signing if he leaves.
With the French international buyout clause to fall from €200m to €100m in the New Year, he will have the choice of destinations.
Manchester United has been the favourite to land the Atletico Madrid striker but the recent report from Spain suggests that Real Madrid president Florentino Perez is also interested in signing the former Real Sociedad frontman, according to Diario Gol.
Griezmann is prepared to move to the Santiago Bernabeu, but only on the condition that Florentino makes room for him. And it's been claimed the president has assured the Frenchman that Gareth Bale will be moved on to make room for him next season.