Griezmann will leave Atletico this summer after five years in the Spanish capital.
The striker was heavily linked with a move to Barcelona last summer, but the transfer fell apart after he decided to stay at Atletico.
He controversially released an hour-long documentary showing behind-the-scenes footage of his deliberation process.
In the end, he signed a new deal at the Wanda Metropolitano stadium, and looked set for a lengthy stay.
However, towards the end of the season speculation began to arise suggesting that he regretted his decision and wanted to leave.
Before the end of the season, Griezmann confirmed in a video on the Atletico Madrid website that he had decided he wants to move on this summer.
Ole Gunnar Solskjaer is keen to revolutionise the squad before pre-season, and has been backed to follow up his signing of 21-year-old Daniel James with moves for Aaron Wan-Bissaka and Matthijs de Ligt.
Despite PSG reportedly overtaking Barcelona as frontrunners for Griezmann, Manchester United are still believed to be keen.
Speaking after France’s 4-0 win over Andorra, the World Cup star admitted he could leave Spain after 10 years in the country.
“There’s a need for patience, as it’s still soon,” Griezmann said.
“I want my future to be decided more than anyone, but there’s a need to wait.
“I don’t know if I’ll remain in Spain. Maybe in two weeks we’ll know something.
“I just want to play football and have fun.”
United could look to Griezmann as a potential replacement for Romelu Lukaku, who has been linked with a move to Inter Milan.
New Inter boss Antonio Conte is a keen admirer of the Belgian, and the striker admitted he could leave Old Trafford.
“I have a contract with Manchester United,” he said after Belgium’s win over Scotland.
“I will talk to the club and my agent to make the best decision.”