Griezmann, 26, had been widely reported to be the club's first major summer transfer target, with the France international fuelling talk of a move to Old Trafford in May. Prior to United's Europa League success over Ajax, the France international said there was a "six out of 10 chance" of him joining Jose Mourinho's side, with the club's qualification for next season's Champions League seemingly enhancing those odds.
Cadena Cope's Antonio Ruiz, one of the most reliable Spanish journalists on Atletico Madrid issues, went on to reveal this week Griezmann has informed the club of his decision to leave the Spanish capital this summer.
Despite all signs pointing towards Griezmann joining United sooner rather than later, wide-ranging reports suggest United have cooled their interest. BBC Sport and the Daily Telegraph are among the outlets claiming the Premier League side are now prioritising the signing of a traditional centre-forward to fill the void left by Zlatan Ibrahimovic.
The former Sweden international ruptured both the anterior and posterior cruciate ligaments in his right knee during United's Europa League victory over Anderlecht in April and is not certain to return this calendar year.
United have been linked with a host no traditional no. 9s including Everton's Romelu Lukaku and Andrea Belotti of Torino, but according to Italian journalist Gianluca Di Marzio Alvaro Morata and Kylian Mbappe are Mourinho's preferred options.
It has previously been claimed that United were keen to bring in a new no. 9 and Griezmann as part of a £200m spending spree at the club this summer that would also include the arrival in a new centre-half and a central midfielder.
However, latest reports coming in from Portugal suggest a right-back could also arrive. According to O Jogo, Benfica president Luis Filipe Vieira has flown into Manchester to negotiate potential moves for Nelson Semedo and Victor Lindelof in a deal that would cost United £83m ($107m) for the pair.
Mourinho has already revealed he has instructed Ed Woodward over which players he wants to add to his squad this summer and hopes to get his business done soon.
"Ed Woodward has had my list, what I want, for more than two months, so now it's up to him and the owners," Mourinho said. "I wish Mr Woodward all the success in his work."