About 10 top officials from the Golkar party said at a Tuesday news briefing that it should drop support for Mr Jokowi's rival, ex-general Prabowo Subianto, and back Mr Jokowi if the Jakarta governor is declared winner of last week's disputed election.
Both candidates claimed victory in the July 9 election, the closest ever in the world's third-biggest democracy and most populous Muslim nation. The Elections Commission is due to announce the official result around July 22.
The defection of members of Golkar to Mr Jokowi could be pivotal for him as it could give him a majority in parliament. Without Golkar, those supporting Mr Jokowi command less than 40% of the seats.
Quick vote counts by private groups, which have proven accurate in the past, put Mr Jokowi ahead by about five points. Mr Prabowo, however, has rejected the tallies, pointing to other, less prominent pollsters that show he won.
To switch sides, Golkar members said they would need to oust party chairman Aburizal Bakrie, who pledged his "permanent" support for Mr Prabowo along with other coalition members at a rally in Jakarta on Monday.
"If we change the party leadership, then we will automatically support Jokowi," said senior party official Fahmi Idris, who was at Tuesday's briefing.
Political partnerships are fleeting in Indonesia's young democracy, which emerged 16 years ago from decades of autocratic rule. Politicians and parties often change alliances depending on who is in power.
Golkar, the dominant party for decades under former autocrat Suharto, has switched sides in the past. In the 2004 election, it was opposed to President Susilo Bambang Yudhoyono but joined the coalition of his ruling Democratic Party shortly after he won.
"Golkar has no interest in being an opposition party," Idris said.
There was no sign that the Golkar members had reached out to Mr Jokowi or to his PDI-P party, and no word on how they might respond. Some Golkar parliamentarians said they would wait for the official election result.
"If Jokowi wins, yes then we should support Jokowi," Agung Laksono, Golkar's deputy chairman, told reporters last week. Mr Laksono is one of the candidates being considered to replace Bakrie as chairman.
Mr Bakrie denied the party would switch sides.
"If you look at the organisation, who has the votes?" Mr Bakrie told reporters on Monday. "I understand that the people (who want to go to the other side) are people who do not have the votes in the party."
But some Golkar members said the party should back a Jokowi administration as his vice president would be Jusuf Kalla, a senior Golkar official and former head of the party.
"As loyal party cadres, it's only natural that we hope the ticket with a Golkar member is successful. We hope the next Golkar leadership will support Jokowi and Jusuf Kalla," said Ginandjar Kartasasmita, a senior party official.
Mr Kartasasmita said he had the support of the majority of Golkar members, but fewer than a dozen senior party officials were at Tuesday's briefing.
Before the election, Golkar was widely expected to back Mr Jokowi because he had made Mr Kalla his running mate.
But Mr Bakrie ended up siding with Mr Prabowo after the candidate promised a senior cabinet position and at least six other ministerial jobs in return for Golkar's support.
That has caused rifts within Golkar, forcing Mr Bakrie last month to expel a handful of members who vocally backed Mr Jokowi.
Golkar needs support from two-thirds of the party's provincial chapters to call an emergency meeting for a leadership vote. A chairman will be chosen by a simple majority.