The organisation's chief executive Stefano Domenicali has met with Thailand's Prime Minister Paetongtarn Shinawatra to begin early discussions about a race in the city from 2028.
The government will now commission a feasibility study into hosting a street race in the kingdom's capital.
In a post on X, Shinawatra said: "We had the opportunity to discuss the opportunity of Thailand to host the Formula 1 race, which is a great sport with a worldwide following.
"The government confirmed that it will study this joint investment, including the study of the race route, the investment budget, and the value for Thailand to receive from hosting the race."
Hosting a race could allow Bangkok to upgrade its infrastructure, as well as bringing in more tourists.
The prime minister added: "I believe that all Thai people will benefit from organising this event, whether it is large-scale infrastructure investment, job creation, new income generation, and importing new technologies and innovations.
"I am confident that this project will be successful. It is another important opportunity for the country to organise a world-class event."
Meanwhile, F1 boss Domenicali described the plans as "impressive".
He said: "I am looking forward to continuing our discussions in the weeks and months ahead."