Griezmann announced last month that he will leave Atleti after five years in the Spanish capital and Barcelona have been favourites to land the 28-year-old for much of the summer.
However, recent reports suggest that Barca are now stalling over a bid for Griezmann and have switched their attentions to PSGs Neymar, 27, and Valencias Rodrigo, 28, instead.
Rodrigo would be a much cheaper alternative and theres a feeling among some inside Barcelonas boardroom that securing a deal for Griezmann – who has a £108million release clause in his contract at Atletico – would be more hassle than its worth.
According to The Sun, Barcelonas hesitance has alerted United to the situation and the Premier League giants are lining up a huge offer for the France international.
The report claims that the Red Devils are prepared to smash their transfer record with a £95m bid for Griezmann.
Griezmann was on the brink of a move to Old Trafford in 2017 before Atleticos transfer ban was upheld meaning they were unable to find a replacement.
United know Griezmann will be put off by their failure to secure Champions League football, but the clubs willingness to satisfy his £450,000-a-week wage demands could give them the edge.
Following Frances 4-0 victory over Andorra on Tuesday night, Griezmann brushed off speculation linking him with Barcelona by suggesting that his future may lie outside of Spain.
Theres a need for patience, as its still soon, he said.
I want my future to be decided more than anyone, but theres a need to wait. I dont know if Ill remain in Spain.
Maybe in two weeks well know something. I just want to play football and have fun.
Ole Gunnar Solkjaer is yet to be convinced by Romelu Lukaku and the Belgian has been heavily linked with Inter Milan following Antonio Contes appointment at the San Siro.
Asked about the rumours, Lukaku told Premium Sport: Its good to see Conte joined Inter, for me he is the best manager in the world.