Barca are keen to sign a new forward before Tuesday's 11pm deadline and are also looking to offload Griezmann, who is currently one of the club's highest earners.
Atletico would be interested in re-signing the Frenchman, though they have been reluctant to let Felix leave in the opposite direction.
According to ESPN, talks between both parties have now broken down and the potential swap deal is now unlikely at such a late stage in the transfer window.
The report states, however, that Atletico are still prepared to negotiate a deal to sign Griezmann, with a £43m bid believed to be on the table.
Another option for Atleti could be to agree an initial loan deal for the 30-year-old forward, with a chance to make the deal permanent in the summer of 2022. body check tags ::