Australia has been criticised by international human rights groups over its slowness to act on same-sex marriage.
Several countries, including Canada, the United Kingdom, United States, France, New Zealand, Ireland and South Africa, have already amended their marriage laws to recognise same-sex unions.
The Daily Telegraph reported on Saturday that the plebiscite, which Turnbull had promised to hold this year, had been delayed until at least February, but a spokesman for the prime minister said no date had been set.
“Late last week the AEC provided advice to the Special Minister of State that strongly recommended against the conduct of a plebiscite this calendar year,” the spokeswoman told Reuters.
“The government has always said that a decision on same-sex marriage will be made by a vote of all Australians in a national plebiscite to be held as soon as practicable.
"That commitment has not changed. The mechanics of the plebiscite, including the specific question and also the timing, are subject to the usual cabinet processes. No decisions have as yet been made.”
The Daily Telegraph reported that Turnbull would reveal his timeline for the plebiscite at a party room meeting of the ruling coalition on September 13.
A leading gay rights advocate and former judge last week urged Parliament to prevent the popular referendum on legalising gay marriage.
Michael Kirby, a former High Court judge who headed a United Nations inquiry into human rights abuses in North Korea in 2014, wrote in The Australian newspaper that a popular vote against gay marriage would likely set back the cause of marriage equality for decades.
Kirby, a 77-year-old who has been in a same-sex relationship since 1969, urged the new Senate to reject legislation that would allow the plebiscite.
“Defeat in a plebiscite on same-sex marriage would kill the reform, probably for decades,” Kirby wrote. “A defeat in Parliament alone would do no more than delay the inevitable.”