Mr Perrett denied reports he was one of two Labor MPs Warren Entsch said he had spoken to about a bill separate to the one Opposition Leader Bill Shorten will table in parliament on Monday.
"There's only one bill going into Parl House: billshortenmp It will be bipartisan and owned by all if Libs vote freely for it," he tweeted on Friday.
Meanwhile, Tony Abbott's sister, who is engaged to a woman, is confident same-sex marriage will be legal in Australia by the end of 2015.
Christine Forster said the successful Irish referendum had been a watershed moment.
It has sent a message to opponents that gay marriage was inevitable if it could get up in Ireland, which previously was "virtually a theocracy".
Ms Forster played down the irony of gay marriage being legalised under her deeply religious and conservative brother's watch.
"He is a wonderfully generously-spirited man," she told ABC TV of the prime minister.
Mr Abbott has agreed to attend her wedding, she said.
Mr Entsch has spoken to a number of Labor MPs, Greens and independents about a cross-party bill, and will also have discussions with his own colleagues.
"It's just a matter of finalising it," he told ABC radio.
The prime minister had asked him to come back with a proposal, Mr Entsch said.
He flagged the intention was to have a bill debated in the August parliamentary sittings.
"I'd like to do this in a very civil and dignified way."
The Queensland MP believes the mood inside the Liberal partyroom has shifted towards a conscience vote.
Australian Marriage Equality spokesman Rodney Croome hasn't lost hope over the prospects of a cross-party bill.
"Ireland has brought this into focus for many people partly because many Australians have a special place for Ireland in their hearts," he told ABC radio.
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