Griezmann, 34, has been weighing up a potential move to the Florida club before the MLS transfer window shuts in late March, but now appears likely to remain in the Spanish capital.
"I stand by what I said (previously), he has a contract with us, he will continue with us," Alemany told Movistar ahead of Atletico's LaLiga match against Real Sociedad on Saturday.
"For him, there's nothing new; we've gone full circle, and we're back to the beginning, where we were before."
Griezmann, who won the World Cup with France in 2018, has a contract with Atletico until June 2027.
The forward is a known admirer of American sports and has long been linked with a move to MLS.
Orlando City own Griezmann's 'discovery rights' - an MLS mechanism giving one team the priority to negotiate a player's transfer, a source close to the discussions told AFP last week.
Griezmann has been rotated a lot by coach Diego Simeone this season and began the match against Real Sociedad on the bench.
Atletico ousted Barcelona in the Copa del Rey semi-finals this week, reaching the April final in Seville, where they will face Real Sociedad.
Simeone previously said Griezmann should choose what suits him best, but hoped that the forward would stay and feature in the final.
Griezmann, Atletico's all-time top goalscorer, last won a trophy with the Rojiblancos in 2018 before an ill-fated switch to Barcelona and subsequent return.
