Vietnamese Prime Minister Nguyen Tan Dung announced on Thursday that his country was pulling out of hosting the 2019 Games because of economic "difficulties".
Olympic Council of Asia (OCA) members confirmed to AFP that Indonesia was now the leading candidate but said more negotiations would be needed.
"The Indonesian people would be proud of being the 2019 Asian Games host country after it held the Games several decades ago," the Indonesian Olympic Committee (KOI) official Ade Lukman told AFP.
"It is very important for Indonesia if we are nominated as the Asian Games host country, as it will help create stronger interest in sports here and hopefully it will help improve the achievement of our athletes competing in the event," he said.
Staging the world's second biggest multi-sport event after the Olympics requires hundreds of millions of dollars of investment.
"The Jakarta authorities have asked questions about the cost," said one OCA official, who spoke on condition of anonymity.
Indonesia is one of three countries that have since shown an interest in hosting the event, the other two are also from East Asia, a source familiar with negotiations told AFP.
"Indonesia, which was beaten by Vietnam in the hosting vote in 2012, is seen as the strongest candidate," the source said.
Mr Lukman said he was awaiting official confirmation of the situation from the OCA.
If Indonesia is selected as host, the event will take place in the country's second biggest city of Surabaya on eastern Java island, he added.
Mr Lukman said that the city administration has expressed its seriousness in building a new sports facility in order to meet requirements for holding the international sports event.
OCA director general Husain Al Musallam said earlier that a final decision on the new Games host country will be made on Sept 20 in Incheon, South Korea, which will host this year's Asiad at the same time, according to
Indonesia staged the Asian Games once before, in Jakarta in 1962.