The French star has been widely expected to leave the Spanish capital club in the next year after a deal with United fell apart in June in the wake of Atletico's transfer ban, and Barcelona have now surged well ahead in the pursuit of his signature.
The Catalans, who are intent on undertaking a major team restructuring after the controversial exit of Neymar, badly want to add more mobility to their attack and see Griezmann as one of the best potential options.
While United's interest in the 26-year-old has cooled since the summer, the club hierarchy has naturally started looking at potential future targets for the close-season.
While the prospect of Griezmann had been raised again, it is understood that word has got back to Old Trafford that Barca are "very far ahead". That is not particularly seen as a concern as United are considering a few options for the summer, in different positions.
The Independent has also been told that some Atletico players now think Griezmann will end up at Camp Nou, too. The French international did sign a new contract in June after the United move collapsed, but it is felt that will merely boost his price, and that Barca will likely have to pay well over £100m.
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