The France forward has been Jose Mourinho’s top summer target, and the deal looked set to be completed during the off-season.
However, according to reports, Griezmann got in contact with the Old Trafford club to say he wouldn’t be joining after Atletico Madrid saw their transfer ban upheld.
The Court of Arbitration for Sport confirmed news of the ban, which prevents Diego Simeone’s men from being able to register new players until January.
This puts Atleti, who had been eyeing moves for Alexandre Lacazette and Diego Costa to replace the 26-year-old next season, in a very difficult situation.
And the France international does not want to leave the club in this predicament, according to El Partidazo de COPE.
However, despite this set-back, Giggs doesn’t think it is confirmation that the deal is off as United are in desperate need of a forward.
“I’m not so sure if we’ve heard the end of that. I think it’ll be ebb and flow during the summer, there’ll be lots of rumours,” the Wales legend told Sky Sports.
“United need goals. All the teams I played in there were goals from everywhere.
“Sometimes you’d rely on a centre-forward for a season, but more often than not you had midfielders, even defenders, wingers and obviously the forwards all contributing.”
Following the news of the ban, Griezmann took to Instagram to post a picture of himself, hinting that he would be staying in Spain.
Alongside the image he wrote: “Now more than ever #Atleti #Alltogether”.