That leaves the Austrian race at Spielberg on July 5 as the second still on the schedule after the French Grand Prix on June 28.
“We don't want to get in the way,” Kogler told reporters when asked if the government would allow the race to take place.
However, he said it was different to staging a football match without fans because of the number of technical staff involved.
The 10 Formula One teams each have about 60 people in the paddock on race weekends while Formula One staff, plus technical and safety officials as well as media and broadcast personnel, would bring the total attending the race to more than 1,000.
The number would increase further if the usual support races, such as Formula Two, were also run.
Kogler added that travel restrictions could be a bigger hurdle than social distancing rules.
“This must then be considered within the framework of the existing restrictions on entry and exit (into the country)," he said. “I don't want to anticipate if an exemption will be needed here or there.”