Jose Mourinho's side have long been seen as frontrunners to sign the France international, who has a €100 million release clause, but his adviser Eric Olhats insists nothing is certain.
And Olhats, who discovered Griezmann as a teenager and brought him to Real Sociedad, says United failing to reach the Champions League would be a significant stumbling block.
"It is quickly figured out that there are not 50,000 clubs that can put €100 million on the table," Olhats said to RMC.
"That is the price of the clause, they won't give anything away cheaply and that limits the number of candidates right now.
"I had heard that Manchester United was done, was signed, but we don't even know if they will play in the Champions League. That is important, I must say.
"Manchester United have made an approach to inform themselves, just like all the others. They come to find out what our thinking is, what the player's thinking is, if there are possibilities, how much, how. It seems logical."
He said: "Chelsea, Manchester City, Barcelona and even Real have knocked on the door to see where things are. Everyone comes to see what is doable, and what is not doable, that is normal. It is a game of musical chairs."
While Griezmann is considering his options, staying at Atletico – where he is contracted until 2021 – remains a big possibility.
"Everything that is put on the table right now, we are thinking about it," said Olhats.
"But I often hear that he needs a team that plays, where he defends less. Except that each year, Atletico Madrid are there or thereabouts. They have reached two Champions League finals, they won the league."
However, issues over a potential switch to Atletico's city rivals and the fact Paris Saint-Germain have not been in touch represents a boost to the other clubs in the race for the 26-year-old.
"Real is impossible," added Olhats. "There is a non-aggression pact, a deal between the two clubs that they do not touch each other – it has been around for a long time. So that is not on the agenda.
"And we have not had any concreate approaches from Paris Saint-Germain as we did the year before.
"Of course we are thinking about things because people are knocking on the door."