Sean Bratches has warned Zandvoort that the venue needs to secure its place on the 2020 calendar.
Earlier this week, Dutch GP boss Jan Lammers said a widely reported March 31 deadline is actually more of a "guideline".
But Bratches, Liberty Media’s commercial boss, told the Dutch publication Formule 1: "Let me put it this way. If the place is gone, it will be gone for five or ten years."
He said negotiations with the organisers of a race at Zandvoort for 2020 are "ongoing".
"We are trying to do a deal but I have heard there is a lot to be done still," Bratches added.
When asked if the March 31 deadline is firm for Zandvoort, he answered: "We are putting together the calendar for next year.
"The requests for grands prix are much higher than the number of places we have available. We have enough to choose from," said Bratches.