The France international re-joined Atletico in August on an initial loan with an obligation to buy after spending just two years at Camp Nou.
Barcelona spent €120 million ($188.5 million) to sign Griezmann from LaLiga rival Atleti in 2019, but the 30-year-old never managed to recapture his best form in Catalonia.
He made 102 appearances for Barca in all competitions – six more than any other player during his time at the club – and was directly involved in 51 goals.
Only Lionel Messi (106), who himself departed for Paris Saint-Germain in the previous transfer window, scored and assisted more goals for Barca over that period.
However, it was at Atletico where Griezmann had the most prolific spell of his career when scoring 133 goals in 257 games between 2014 and 2019.
The Real Sociedad academy product has scored eight goals and assisted two more in 19 games since returning to Atletico – no Atleti player has been involved in more goals.
Back playing where he feels most comfortable, Griezmann sees no reason to move away from the Spanish capital for a second time.
"The truth is that I performed well at Real Sociedad, then I grew athletically and also privately at Atleti, with my wife, with my children ... That helps you be more relaxed and enjoy everything," he told Transfermarkt.
"Then I went to Barcelona. Because of the circumstances, things didn't go as well as I had hoped. That's why I wanted to come back, to play for Cholo [Diego Simeone] and Atleti again.
"That's what I wanted the most, and the truth is that I'm really enjoying it here and I hope I can continue like this.
"I hope Atleti want me as long as I can keep up with the pace of the games and the demanded level, and that we can write another beautiful story."
Griezmann has been linked with an array of European heavyweights in the past, including Bundesliga champion Bayern Munich, but he has not considered a move to Germany.
"I've never thought about it, because since my time at Real Sociedad I've always felt comfortable where I was, and in the end, I feel most comfortable and happy here at Atleti now," he said. "I don't want to move again."
This week marks 10 years since Simeone took charge of his first Atletico match and no player has scored more goals under the Argentinian coach.
Indeed, Griezmann's 141 goals is the fourth-most in Atleti history and the forward credits Simeone with getting the most out of him.
Asked which of the coaches he has worked under has impressed him most, Griezmann said: "I would say it's Cholo. I think he's the coach who knows me best.
"I have an incredible relationship with him, and also on a sporting level he has always fought with the best, in the Spanish league or in Europe. He has taken the club to the highest level possible."
Atletico faces Villarreal in its next LaLiga fixture on Monday (AEDT).