"With Real Sociedad, I felt I needed to leave," Griezmann told RMC Sport.
"For now, I don't have this need or that desire. We don't know how the season will end.
"If it ends badly, maybe I'll ask myself the question. For now, it's not relevant."
Along with United, Chelsea are also reportedly interested in signing Griezmann – who finished third in the 2016 Ballon d'Or.
But while Griezmann likes the intensity of the Premier League, he is unsure about the lifestyle in England.
"Afterwards, I wonder where I can leave to. In Spain, there is Barca and Real Madrid," he said.
"Barca have the front three [Lionel Messi, Luis Suarez and Neymar]. Madrid is impossible because of my club. I believe they have a pact between them.
"Germany, it's not a championship that attracts me. France, not for the moment.
"And England, there are many doubts about my private life. There is rain, bad weather... I need to be happy outside."
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