The Argentine coach had been expected to lead Atleti into their new stadium at La Peineta when the season begins in August, though Manchester United's interest in France international Griezmann has been a cloud lingering over the club.
And now Simeone has revealed that 'Grizou' offered to remain with the club if the coach would give similar assurances, only for Simeone to be non-committal.
"Griezmann said to me: 'if you stay, I'll stay,'" the Atleti coach revealed.
"But from here forward nobody knows what is going to happen.
"I would never force him to say."
Atletico are expected to secure the signing of in-demand Lyon forward Alexandre Lacazette this summer if successful in appealing their transfer ban.
But the France international would then be competing with fellow Bleus Kevin Gameiro and Griezmann for a spot in the side.
While Lacazette has been reportedly pursued at the behest of Griezmann, the club are aware that they would be powerless if Man United met his €100m release clause, something the Red Devils are willing and able to do.
The fear in the United camp is, however, that Griezmann is still trying to negotiate a move to Atletico's cross-city rivals Real Madrid.
Simeone also revealed that he turned down a £35m contract to leave Atleti.