The France superstar has been regularly linked with a move to Old Trafford, while a shock move across the city to Los Blancos has also been mooted.
But it remains to be seen if Griezmann, who has a €100million release clause in his contract, will be with the club next season and his advisor Eric Olhats says several avenues are being explored, with United's offer the "first" to arrive.
"There is an existing clause of €100million which is unavoidable," he told Telefoot. "We're thinking right now about the most suitable offer. Real Madrid and other clubs are part of this thinking process.
"Antoine doesn't want to leave the club at any cost. That is false. We are going to observe.
"There is Manchester United, they told us about their project. They were the first and the most solid in their enquiry."
"No, no contact with PSG," he added. "Last year, there was a real interest. Not this year. He might not be in their plans anymore."