The Atletico Madrid forward has been linked with a move to the Camp Nou in recent weeks, while United has been on the radar since the summer. He was close to joining the Red Devils but chose to stay at the Wanda Metropolitano stadium for another season owing to the club's transfer ban.
Griezmann has struggled for form this season compared to his last two campaigns, but is still highly sought after. The Catalan giants look eager to sign him as Barcelona head of sporting and institutional relations Guillermo Amor hinted that they had already approached the forward about a potential move, which has now been reported to Fifa as Atletico had not given permission to hold talks.
Barcelona are now favourites to land the striker after recent reports suggested that United have ended their interest in signing the France international. Mourinho is said to be a fan of the player, but does not believe Griezmann is worth his hefty release clause, which was believed to be €100m (£88.7m).
However, Atletico chief executive Miguel Angel Gil Marin has now revealed that the former Real Sociedad's release clause is €200m until 1 July 2018, which is likely to keep interested suitors away at least until the next summer's transfer window.
Diego Simeone opened the door for Griezmann's exit by stating that he could be allowed to leave at some point, but Atletico's CEO has made it clear that they have no intention of selling him either in January or next summer. He admitted that they are looking forward to Griezmann partnering Diego Costa in attack in the New Year when the former Chelsea striker can finally play after the club's transfer ban comes to an end.
The latter joined the Spanish capital club in the summer, but was unable to play due to the ongoing transfer ban. Apart from Costa, they will also welcome winger Vitolo, who has been plying his trade with Las Palmas in the first-half of the campaign.
"Atletico doesn't want to sell Griezmann either now or in the summer," Gil Marin said, as quoted by Goal. "For us he is a very important player, who has grown a lot and we have grown up with him.
"Our intention is to keep growing all together. Last summer we made an effort beyond the possibilities of the club and we'll do it again next summer. Griezmann departure isn't in our hands, but until summer is impossible to leave us," he added.
"It's been hard for us to get Griezmann and Diego Costa together and I think it's going to be very good for Atletico.
"Until July 1, Griezmann's release clause is €200m," he explained after initial reports suggested that the striker's release clause will drop to €100m in January.