His remarks were the first on the topic, which was mooted by Deputy Energy Minister Widjajono Partowidagdo in November.
The Batam power plant idea aims to reduce Indonesias gas exports to Singapore, and divert the gas to local industries in Java instead.
The Indonesian government has two long-term contracts with Singapores SembCorp Gas and Gas Supply to supply the city with gas from fields in South Sumatra and the Riau islands through undersea pipes until 2023.
"If that [the Batam power plant] would serve as a solution, we could proceed with it," Yudhoyono said during a news conference on Monday night. The plan is now being evaluated by the energy ministry.
The plan comes just as Singapore is planning to import electricity directly. Singapore now generates all of its electricity - 80 per cent of which relies on imports of natural gas from Indonesia and Malaysia. The other 20 per cent is generated from other sources such as fuel oil, diesel and waste incineration.
The plan to import electricity - likely starting in 2017 or 2018 - is part of a larger effort to increase and diversify Singapores energy sources, which could include nuclear energy in the future.
Kurtubi, director at the Center for Petroleum and Energy Economic Studies, said the project, if approved by Yudhoyono, would likely get the nod from Singapore to amend existing gas sale contracts.
"Indonesia can convince Singapore that this way, they will get a very long-term supply of electricity because Indonesia has abundant coal," said Dr Kurtubi, who goes by only one name.
The best locations for the power plants are in Pemping and Kepala Jeri islands, where undersea electricity transmission cables to Singapore can be most economically built, said Ahmad Hijazi, head of Batams industry, trade and mineral resources department.