Griezmann featured in all five of France's games in Brazil as Didier Deschamps' men exited in the quarter-finals, losing out to Germany in a 1-0 last eight defeat on Friday.
The 23-year-old's impressive displays have seen him linked with a move away from Anoeta, but Aperribay would not be drawn on the subject at a media conference on Saturday.
"We will hear from Griezmann to see what is his will," he said.
Aperribay was speaking at the presentation of Carlos Vela and Alfred Finnbogason.
Vela recently put pen to paper on a four-year extension at the club, bringing an end to speculation linking him with former club Arsenal, while Finnbogason arrived from Heerenveen earlier this week.
"The continuity of Carlos was a priority," added Aperribay. "Carlos chose Real and we want to thank him for his decision.
"We have been following Finnbogason since last year. The talks with his former club began in May.
"They are two great players. We already know Carlos, and Alfred will show it."
