The world’s largest publicly listed oil company is bidding for the Pasangkayu and Surumana areas, according to Exxon’s Indonesian unit president Maman Budiman.
The Indonesian government is expected to announce the block winners by next week.
Budiman said the company believes there is potential for undiscovered hydrocarbons in those areas.
He added the company will continue to invest in new areas of Indonesia, despite long-running negotiations and disputes over the $US2.6 billion Cepu Block.
Exxon Mobil is still in talks with state oil company, Pertamina, over control of Cepu – the nation’s biggest untapped oilfield.
The four-year dispute had appeared close to resolution after the companies signed a 30-year production-sharing contract last September.
But Exxon insists on being the sole operator for the project, while Pertamina wants the two companies to operate the block in five-year rotations.
Pertamina chief executive Widya Purnama said in November that his company refused to hold further meetings with Exxon.
Containing estimated reserves of about 600 million barrels of crude oil, Cepu has the potential to rejuvenate Indonesia’s flagging oil output.
Indonesia’s oil production has fallen in recent years due to a lack of investment in oil exploration and production.