There is a dispute, though, over which club initiated the talks, identified the players involved, and ultimately rejected the idea.
The newspaper Marca first reported the conversations in a frontpage story on Friday, calling the move "the impossible exchange."
ESPN has confirmed that those discussions happened, and that a deal was quickly dismissed, with both clubs pointing the finger at each other.
Sources close to Atletico told ESPN that Barca suggested the swap as they look to reduce their wage bill, with Griezmann reportedly earning five times as much as Felix -- but the Rojiblancos, unwilling to let the Portugal teenager go, immediately rejected the idea.
However, sources in Barcelona told ESPN that conversations took place, but it was Atletico who proposed a return for Griezmann, in exchange for other players not including Felix, and it was Barca who turned the offer down.
The two clubs found themselves in precarious financial positions this summer, with Barcelona looking to bring in €70 million in player sales, and Atletico also needing to sell before strengthening their squad.
Griezmann, who was one of Atletico's key players in a five-year spell at the club, announced that he was leaving the Wanda Metropolitano in May last year. Two months later, Barcelona paid his €120m buyout clause.
It was an acrimonious departure, with Atletico having claimed they were owed an additional €80m as the deal had effectively been agreed earlier, before the clause dropped from €200m.
Atletico fans later sang "Griezmann die" when the clubs met in La Liga in December, holding up a banner saying "You wanted to have a name and you forgot to be a man."
He went on to have a solid, if unspectacular, debut season at Barca, scoring nine league goals and was named a sub in their 8-2 Champions League thrashing by Bayern.
Griezmann's camp remain confident that he will find his best form in his second season at Camp Nou, sources told ESPN, and have been reassured that the club view him as a key member of Ronald Koeman's team going forward.
He also had an underwhelming season, scoring six times in La Liga during a campaign disrupted by injuries.
Felix was left out by coach Diego Simeone in the Champions League quarterfinal defeat to Leipzig, coming off the bench to score a penalty equaliser before the Germans' late winner.