It comes after a meeting with International Olympic Committee (IOC) president Thomas Bach on Saturday, BBC Sport reported.
The country is currently hosting the Asian Games – the world's second-largest multi-sport event after the summer Olympics – which comes to an end today with the closing ceremony in Jakarta.
India, Australia and China have also expressed an interest in bidding.
"After the excellent experience of the Asian Games we now believe we can host the very biggest sporting event," Widodo said.
About 12,000 athletes from 45 nations competed in Indonesia across 60 different sporting disciplines.
The Asian Games were only awarded to Indonesia four years ago after Vietnam pulled out for financial reasons, and the standard of organization has been widely praised.
IOC president Bach welcomed the Indonesian candidacy, adding that the Asian Games provided a "strong foundation" for the country's 2032 bid.
"Because with this Asian Games, with this great success, Indonesia has shown that they have all the ingredients to hold the Olympics successfully," said Bach.
"Here in Indonesia there is a great combination of friendliness and efficiency and this is what the Games are about."
Tokyo, the capital of Japan, will host the 2020 Olympics and Paralympics, with French capital Paris and American city Los Angeles hosting the 2024 and 2028 Games respectively.
The Indian Olympic Association has already confirmed its interest in bidding for 2032, as has Chinese city Shanghai, despite China's capital Beijing hosting the summer Games in 2008 as well as the 2022 Winter Olympics.
Neither India nor Indonesia have ever hosted an Olympic Games before.
Australia, who last hosted the Games in Sydney in 2000, is reportedly planning a Brisbane bid.