Liberty Media is in talks with Saudi Arabia about a grand prix in the controversial Kingdom for 2021.
London's Times newspaper reveals that talks between Saudi officials and F1's owner have taken place "several" times.
Correspondent Rebecca Clancy also said the "teams have been asked for their views" about racing in Saudi Arabia, which is often accused of human rights violations.
But the expansion of the currently 21-race calendar to 22 races next year and then even more in 2021 and beyond will also be controversial.
Claire Williams confirmed: "We are incredibly worried about the prospect of having 24, 25 races on the calendar.
"Asking the people who work for us to travel as much as that is a huge undertaking," she said.
"Bringing new parts to 21 races is hard work, bringing new parts to 25 is going to bring even more pressure on our businesses, so that for me is a huge concern."body check tags ::