Barca failed with an offer to take Felix on loan Monday, with Atletico knocking them back immediately, but returned on Tuesday with a new proposal involving Griezmann.
Felix's agent, Jorge Mendes, is working as an intermediary in the talks, and sources close to Griezmann told ESPN a return to Atletico is not "impossible."
However, sources told ESPN it would be difficult for Felix to leave at this stage of the window as coach Diego Simeone does not want to lose him. Atletico, though, would be willing to reopen talks over exchanging midfielder Saul Niguez for Griezmann.
Sources indicated to ESPN that Barca would not want to lose Griezmann without guarantees that another forward was coming in.
ESPN revealed earlier in the summer that the two clubs had held talks over a potential swap deal involving Saul and Griezmann. Those talks broke down because of the difference in valuations of the two players.
At the time, Griezmann was open to returning to Atletico, whom he left for Barcelona in 2019 for a fee of around €120 million.
Simeone is keen to work with Griezmann again, although sources indicate not at the expense of Felix. The France forward, 30, spent five years playing under Simeone before moving to Camp Nou, scoring 133 goals in 257 appearances.
Felix, 21, joined Atletico as Griezmann's replacement two years ago, signing for €126m from Portuguese side Benfica. He has scored 19 goals in 76 games in two seasons at the Wanda Metropolitano.
Saul, meanwhile, has also drawn interest from Chelsea. ESPN revealed last week that the English club approached Atletico regarding a season-long loan with an option to make the deal permanent down the line. Manchester United have also shown an interest.
Barca's activity in the transfer window this summer has been limited because of their financial problems. President Joan Laporta revealed recently that their gross debt stands at €1.35 billion. Sergio Aguero, Memphis Depay and Eric Garcia have all arrived on free transfers, while €9m signing Emerson Royal is set to join Tottenham on Tuesday in a deal worth a potential €30m.
Lionel Messi, Junior Firpo, Francisco Trincao and Konrad de la Fuente are some of the other players who have left this summer, freeing up some space on the wage bill with coach Ronald Koeman asking for another forward.