Manchester City and Chelsea have also been linked to Griezmann at times, but Manchester United remain the frontrunners for his signature.
'I can not say yes or no, otherwise I will be in the sh**,' he said.
He said: 'I do not rule out anything in the future, but I'm happy at Atletico and hopefully I can stay here.
It has been reported that Man United manager Jose Mourinho has made the 26-year-old his number summer transfer target, but Atleti won't let him leave without a fight.
The Sun quotes the 25-year-old, whose late goal grabbed Atletico Madrid a share of the spoils in Saturday's derby against Real, spoke after the game and explained that it would be nearly impossible to make the a move to the Bernabeu. "For this reason, I think it's dead", he added.
Real Madrid captain Sergio Ramos has said the club's "doors are always open" to the best players, putting Atletico Madrid forward Antoine Griezmann among that group.
Reports in Spain say Atletico have reacted to the latest speculation over Griezmann's future by offering him a new contract that would pay €10 million a year, with his €100 million release clause being raised.
'We are happy to get these calls but for now, I am happy here and in a good mood.
The Atletico Madrid ace is set to be one of the most coveted players in European football this summer. When we speak about Real and Atletico, it is not good for the fans or the club.
Atletico coach Diego Simeone conceded after Saturday's game that he is unsure where Griezmann, who has a contract at the Vicente Calderon until 2021, will end up.
Where do you think Griezmann should play next season?