The Atletico Madrid striker announced his intention to leave the La Liga club one month ago.
“It’s been an incredible five years. Thank you for everything,” he said.
“I wanted to tell the fans who have always given me a lot of love that I have taken the decision to leave, to see other things, to have other challenges.”
Griezmann was expected to join Barcelona last summer, and once again, speculation is rife that he will join Lionel Messi at the Nou Camp.
The World Cup winner gave the Red Devils hope when he claimed that his future may now lie away from Spain.
Speaking after France’s 4-0 Euro 2020 qualifying win in Andorra on Tuesday, he said: “I don’t know if I will stay in La Liga.
“I know where I want to go. I am also keen to get this over with as quickly as possible.”
Barcelona are eyeing a mega-money return for Neymar who quit the Catalan club to join Paris St-Germain in 2017.
And that could leave the door open for United to swoop and land Griezmann, despite not being able to offer him Champions League football next season.
The report says United are willing to pay his transfer fee and meet his staggering wage demands of around £450,000 per week.
But some supporters are far from convinced that a £95m transfer is plausible in the first place.
And other fans have big reservations about whether the Frenchman could cut it in the Premier League.
One wrote on Twitter: “We’ve been linked with 43 players since the end of the season and most of them, like in this case, are just stupid rumours.”
Another worried supporter simply wrote: “PLEASE GOD NO!”
“Just after the CEO of Atletico confirmed that he is joining Barca. Yes… Sure,” added a sceptical third.
A fourth fan ranted: “Ed Woodward, more media links to make it look like the club is trying when really got nothing in the pipeline.”