The news came from the Daily Telegraph's James Ducker:
James Robson of the Manchester Evening News verified the report:
With Zlatan Ibrahimovic on the sidelines and potentially leaving the club this summer, United only have Marcus Rashford available as a senior striking option.
Griezmann racked up 26 goals and 10 assists in all competitions last season, but he often plays in a supporting role or occasionally even out wide rather than as an out-and-out No. 9.
He frequently plays alongside either Kevin Gameiro or Fernando Torres, who typically occupy that role.
The Frenchman has an £86 million release clause, and United will almost certainly have to pay that in order to land him, so it's perhaps understandable they wish to address more pressing needs in the squad before splashing that sort of cash.
That said, it could be argued they need to fill both positions.
Even with Ibrahimovic fit for the majority of the campaign—and the Swede had a prolific season, scoring 17 goals in 28 Premier League appearances—United mustered just 54 league goals in total.
Therefore, even if he is replaced with a similarly potent goalscorer, it may not be enough to significantly improve their attacking output if the new striker is the only addition made up top.
Robson provided further analysis of the situation:
With Atletico's transfer ban upheld, per the club's official Twitter account, they cannot register players until 2018. As such, they would be unable to replace Griezmann until January at the earliest, with any forwards brought in this summer having to sit on the sidelines until then.
Loyalty to Los Rojiblancos might see Griezmann opt to stay put for another year to avoid putting his employers in that situation.
Whatever happens with the France international, it's clear United need plenty more firepower than one man can provide.
Ideally, they will bring in both a No. 9 and a No. 10 this summer—if they don't, they could struggle to kick on.