Jose Mourinho has identified the Atletico Madrid striker as his No1 target come the summer.
And United are said to be prepared to meet his £86million buy-out clause.
But while reports have claimed a deal has been agreed in principle with the France international, European journalist Andy Brassell insists it’s not that close.
Manchester United currently sit sixth in the Premier League table, two points off fourth-placed Arsenal.
Antoine Griezmann's move to Manchester United will collapse without Champions League football
And while Mourinho’s team have improved as the season’s progressed, Champions League football is not a guarantee, and that will prove pivotal to landing Griezmann, according to Brassell.
“There have been reports that a contract has been agreed,” Brassell told BBC Radio 5 Live.
“As far as I can gather, it’s not that far along, but there have been discussions.
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Is this how Manchester United could look with Antoine Griezmann
Antoine Griezmann and Diego Simeone have a good relationship at Atletico Madrid
“I don’t think this is as open and shut a deal as some are suggesting.
“One – because Griezmann’s future is quite tied to that of Diego Simeone, who I think is unlikely to leave at the end of the season and will probably stay for their first season in the new stadium.
“Two – there’s the fact that Manchester United might not qualify for the Champions League.
Jose Mourinho wants France duo Paul Pogba and Antoine Griezmann to link up at Manchester United
There’s no way he’s going there if they don’t qualify for the Champions League
“There’s no way he’s going there if they don’t qualify for the Champions League – that’s really important to him.
“Thirdly, and I think the most important thing, I don’t think he’s a terrific signing for United, and I think he will probably know that.”
Atletico president Enrique Cerezo has also claimed United will not be signing Griezmann, as he said: “I don't know what Manchester United's interest is. But Griezmann will be at Atletico for a long time."