Musk was not immediately available for comment after minister Luhut Pandjaitan made his remarks to reporters.
Musk and Widodo met in Indonesia's Bali after both attended the World Water Forum on Monday.
"We made an offer, is it possible to build an EV battery plant here, precursor cathode. And he will consider it," Luhut told reporters.
Luhut said Widodo also asked Musk to consider investing in an AI centre in the Southeast Asian country and for SpaceX to build a launchpad in Biak island in Indonesia's Papua province, an offer the government has made before.
Indonesia's government has been trying for years to lure Tesla to build manufacturing plants related to electric vehicles as the government wants to develop its EV sector using the country's rich nickel resources.
On Sunday, Musk had launched SpaceX's satellite internet service for the health sector in Indonesia.
Starlink was now available commercially, but the government would focus its services first on outer and underdeveloped regions.
SpaceX's Starlink, which owns around 60% of the roughly 7,500 satellites orbiting earth, is dominant in the satellite internet sphere.
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