Barcelona forward Griezmann has been on loan with Atletico since the start of the 2021-22 season.
The 31-year-old has had his game-time severely restricted this season because of a clause in his loan deal with Atletico, which states that the club must sign the France international permanently if he plays over a certain number of minutes.
It is believed that if Griezmann plays at least 45 minutes in 14 of Atletico's matches this campaign it will trigger the clause, forcing Atletico to pay Barcelona a €40m (£35m) transfer fee to sign him permanently in 2023.
As a result, Atletico Madrid manager Diego Simeone has stopped starting Griezmann in the majority of the club's matches this season, typically bringing him on after the hour mark instead.
However, an agreement has now been reached between Barcelona and Atletico Madrid to reduce the transfer fee to €20m (£17.5m), according to French publication L'Equipe.
Griezmann, who is under contract with Barcelona until 2024, is expected to accept a pay cut to ensure a permanent transfer to Atletico can go ahead next summer.
The World Cup winner currently earns around €12m (£10.5m) per season, according to Get French Football News.
His annual wage is set to drop to €8m (£7m) per season if he joins Atletico Madrid.
L'Equipe claim Griezmann will sign a three-year deal with Atletico until the summer of 2026.
When asked last month about his unusual contract situation, Griezmann said: "It is what it is, it's out of my hands.
"[I'm] grateful to God for being here. My family is happy, I of course want more, but I am going to give everything I have in the minutes I have.
"I feel like a man of the club, I am happy here and I only want to play here and give everything for the club, for Cholo and for the fans."
Griezmann has scored three goals in 10 appearances for Atletico this season despite his lack of minutes.
In total, he has managed 144 goals in 303 games over the course of his two separate spells with Atletico, having played for the club for five seasons prior to his £103m move to Barcelona in 2019.
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