United are reportedly willing to meet his £85million release clause and will use Paul Pogba to try and convince him to move to Old Trafford.
But Spanish football expert Gibson has cast doubt over United's move for the France international with Atletico Madrid's FIFA-imposed transfer ban meaning they would not be able to replace Griezmann should he leave.
Terry Gibson reckons Antoine Griezmann's move to Man United will be less than straightforward
He admits the La Liga side would be helpless should United trigger Griezmann's release clause.
But Gibson reckons the club's ban, coupled with United's scrap for Champions League spot, could make their pursuit of Griezmann less than straightforward.
"We have to look deeper now because there is a lot more talk in England than there is in Spain," he told Sky Sports.
Atletico will be unable to replace Griezmann should he leave due to a FIFA-imposed transfer ban
"As things stand, Atletico Madrid cannot sign a replacement so that surely must influence the decision. Although, if his buy-out clause is triggered there is nothing they can do about it.
"We have to look at where they finish this season as well, whether they finish outside of the Champions League spots – I don't think they will be.
"It's a big ask for Manchester United to try and qualify for the Champions League, I know that didn't deter Paul Pogba but I don't think it's cut and dried.
Griezmann is Jose Mourinho's No 1 summer transfer target
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How Man United could look with Antoine Griezmann
Wed, February 1, 2017
Is this how Manchester United's squad could look with Antoine Griezmann
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Is this how Manchester United could look with Antoine Griezmann
"We haven't heard much in Spain, where they tend to get their transfer speculation from the English papers in any case.
"It's going to be a talking point from now until the end of the season because the window is closed and people cannot cope without transfer news."
Griezmann has scored 15 goals in 30 appearances for Atletico and is contracted to the club until the summer of 2021.