The future of the World Cup winner was the subject of much speculation throughout the last transfer window, with Barca, and Manchester United, strongly linked with signing the 27-year-old.
He has since discussed how it was a difficult decision to turn down Barca but the Frenchman, who signed a new deal with Atleti through to 2023 back in June, was always going to stay, according to Simeone.
"I swear on my kids that I never saw us losing him," he told El Partidazo de COPE . "I never saw him at Barcelona. I always felt like he would stay."
Griezmann's team-mate Jan Oblak, meanwhile, is another Atleti star who has been snubbed for big individual prizes, missing out on the nominees for goalkeeper in the FIFPro World XI awards .
Simeone was asked about Oblak and insists former Atleti loanee Thibaut Courtois, who joined rivals Madrid from Chelsea in the last window, would not get in his team.
"Oblak is the best and at least in the top three keepers in the world," Simeone insisted. "Courtois would not be a starter at Atletico. Oblak is better."
Atletico Madrid, who Simeone has declared are at Real's level following their sale of Cristiano Ronaldo to Juventus, are currently 10th in the Liga table after three rounds of matches.