The country is hosting its third F1 event this weekend in Jeddah, but an additional track is currently under construction near Riyadh.
F1 bosses struck a 10-year deal to race in Saudi Arabia, with the plan to switch venues from Jeddah to Qiddiya, a purpose-built venue 25 miles from the country's capital.
But speaking ahead of Sunday's race on the Red Sea, Prince Khalid, Chairman of the Saudi Motorsport Company said: "Saudi Arabia is a very big market and we have a very strong economy, so the idea of having two races in Saudi is doable.
"I would not be surprised if Saudi in the near future will host two races.
"Formula One is growing and there is a lot of demand here. Saudi is big and the regions are so far away. It is like the United States. There are three races in the US because the market is so big there and there is demand.
"The decision is not made and there are a lot of things that we need to consider. We don't know if it would be practical and feasible for Formula One Management and the teams, but we built this track in Jeddah to last, and in theory we could have two races."
The sport is back in Saudi Arabia, 12 months after a nearby missile strike overshadowed last season's race. The country has also been heavily criticised for its human rights record.
Asked earlier this week if he was unhappy to be racing in Jeddah, Lewis Hamilton cryptically replied: "It is open to interpretation.
"Hopefully everyone has a safer weekend. That's as much as we can do, right?"
Responding to Hamilton's remarks, Prince Khalid said: "I haven't spoken to him, and I have not met him. Everybody has an opinion, and we respect everyone's opinion.
"We think we have a great country, we are changing a lot and we are opening a lot so there is a lot of progress.
"The last thing we want is for someone to come to Saudi who is forced to race by a contract or doesn't feel comfortable.
"We are working very hard to satisfy everyone. It is a difficult task, but we will do our best and hopefully Lewis's opinion will change in a year or two.
"The majority of the drivers are happy to come here, and they are seeing the change and the development. Hopefully we can make Lewis, and other people who think the same, more comfortable in the upcoming years."