The 72-foot (22-metre) boat carrying mostly Tamil asylum-seekers, including women and children, left India two weeks ago and was 175 nautical miles west of Australia's Indian Ocean territory of Christmas Island, the Refugee Action Coalition said.
"We are refugees. We come from Sri Lanka -- we stayed in India and we are unable to live there. That's why we are coming to Australia," a man who claimed to be onboard told the Australian Broadcasting Corporation.
The man, who only gave his first name as Duke, said there were 32 women and 37 children on the vessel which would be, if it reaches Christmas Island, the first asylum-seeker boat to reach Australia in six months.
Immigration Minister Scott Morrison refused to confirm or deny the reports, saying the government had not changed its policy of only commenting when there was a significant incident to report.
"It is our standard practice under Operation Sovereign Borders to report on any significant events regarding maritime operations at sea particularly where there are safety of life at sea issues associated and I am advised I have no such reports to provide," he told reporters in Melbourne.
"There is therefore no significant event for me to report at sea."
Australia's conservative government has a policy of pushing boats back towards Indonesia, where they have traditionally departed from, as part of a range of measures designed to stop people-smuggling.
But refugee advocates said given this boat came from India and had sprung an oil leak, it required assistance.
Refugee Action Coalition spokesman Ian Rintoul said he had spoken to someone onboard early Saturday who told him the boat had made progress towards Christmas Island.
But he said those onboard felt they would run out of oil before making land.
"The main fear is that the boat will stop and they will be vulnerable to the elements," Rintoul told AFP, adding there were no medical emergencies onboard the boat.
"We are quite anxious to confirm that the navy is on the way. The truth is there simply is no time to be lost," he added.
Hundreds of asylum-seekers have drowned making the perilous sea journey to Australia in recent years.
Canberra has toughened its policy on asylum-seekers to deny those arriving on unauthorised boats the ability to resettle in Australia even if found to be genuine refugees.
Instead, they are sent to camps in the Pacific, on Papua New Guinea's Manus Island and the tiny state of Nauru to be resettled there.