Olhats confirmed that he had been in contact with PSG sporting director Olivier Letang in recent months, with the Ligue 1 outfit interested in signing the France international. However, the 25-year-old Griezmann has rejected the advances of PSG in order to remain with Atletico, who have made the Champions League final twice in the last three years.
"There were discussions with Olivier Letang," Olhats told RMC. "There was interest from Paris. We listened because it is all the same a club with objectives and resources.
"After numerous discussions, and drawing a parallel a little bit with other offers, we opted for continuity.
"There were approaches. It's 100 percent certain that he'll be at Atletico Madrid next season. Would it have been wise for him to leave for a club with a bigger scope to win trophies? Barca and Real are fully stocked at the moment.
"Atletico give the impression of a struggle, but I think they're equipped to win trophies."
Griezmann is likely to continue to draw interest from clubs around the world after his performance at Euro 2016, where he finished as the tournament's Player of the Tournament top scorer with six goals.