The Atletico Madrid forward, who scored his side’s equaliser in Saturday’s 1-1 Madrid derby draw at the Bernabeu, is a long-term transfer target for United and several other elite European clubs.
As revealed by The Independent last month, Griezmann has reservations over moving to the Premier League, leaving a switch across the Spanish capital as his only realistic option.
Sunderland 0 Manchester United 3 player ratings
Show all 22
However, the France international believes such a move is unlikely given the historic rivalry between the two clubs.
“I do not rule out anything in the future, but I'm happy at Atletico and hopefully I can stay here,” he said.
“Interest from Madrid? I can't say "yes" or "no". You never know what can happen in football, but moving from Atletico to Real, I don't know if it's achievable.
“Very few players have done so. For this reason, I think it's dead,” he added.
Santiago Solari was the last high-profile player to move from Atletico to Madrid, making the move across the city in 2000.
Several players have turned out as a youth player for one of the Spanish capital’s clubs before switching allegiances, with Raul, the 228-goal Madrid great, being the most famous example.
Register for free to continue reading
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Registration is a free and easy way to support our truly independent journalism
By registering, you will also enjoy limited access to Premium articles, exclusive newsletters, commenting, and virtual events with our leading journalists
Join our new commenting forum
Join thought-provoking conversations, follow other Independent readers and see their replies