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The Frenchman arrived at the Camp Nou from Atletico back in 2019 - who then used those funds to secure a deal for Felix from Benfica.
But Griezmann hasn't lived up to expectations with the Blaugrana and they've gone two consecutive seasons without winning La Liga.
TV3 have claimed a swap deal is 'financially viable' for the two clubs as the pair are said to be on similar wages.
Felix's current agent is Jorge Mendes and the super agent could find a way to engineer a transfer for his client.
Barcelona are looking to replenish their frontline after allowing Luis Suarez to join Atletico last summer - a move which has seen the Uruguayan prove his doubters wrong.
Atletico sit top of La Liga going into the final day and Suarez has scored 20 goals this campaign.
Lionel Messi is still the figurehead in attack, but signing Felix and then playing teenager Ansu Fati will give it a youthful feel.
Felix has only managed 13 goals in the last two seasons and hasn't played a full game since March.
Despite this, manager Diego Simeone stresses the 21-year-old has a key role in his side.
He stated per Daily Mail: "We hope that when Joao Felix is involved, he will give us what he can and show how important he is.
"The team needs him.
"As for Luis, we are now entering Suarez territory. It is the ideal time for a footballer like him to find the solutions to what we might encounter. He's used to this kind of game."
Victory over Real Valladolid on Sunday will confirm Atletico as champions ahead of bitter rivals Real Madrid.
Last weekend was full of drama as Atletico sealed a stunning last-gasp win against Osasuna, while Madrid squeezed past Bilbao thanks to a second-half goal from Nacho Fernandez.
Real Madrid and Atleti players reacting to eachothers live scores in a crucial part of the title race pic.twitter.com/ZDdLvfP4yr- Don B :flag_se: (@Griezass) May 19, 2021
It was a tense 90 minutes for both sides, and footage from the bench shows how the likes of Marcelo and Lucas Torreira communicated with their teammates about results elsewhere.
Do you think Barcelona will sign Joao Felix this summer?
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Featured Image Credit: PA Images
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