The prime minister spent one hour with Tasmanian independent Andrew Wilkie in her official Melbourne office on Saturday, but was coy with the details.
It was left to Mr Wilkie, a former intelligence whistleblower, to explain his push for national gambling laws.
"That was a good meeting," Mr Wilkie told reporters.
"I did emphasise repeatedly that reform of poker machine legislation nationally is one of the most important issues for me personally and it's an area that I expect either the Labor party or the coalition parties to commit to some kind of reform if they are to have my support."
Mr Wilkie said he was hopeful of making a decision about which side to back by the middle of next week.
"It's certainly in the public interest that all of the independents do what I'm trying to do and that is to reach a decision early," he said.
Mr Wilkie, who meets with Opposition Leader Tony Abbott on Monday, said becoming a minister or the Speaker was not his ambition.
He would also refrain from caucusing with the re-elected country independents Tony Windsor, Bob Katter and Rob Oakeshott.
Ms Gillard has already met with the three former National Party members, and has sat down with lower house Greens MP Adam Bandt.
A week after the election, counting has resumed in the only close seat - Brisbane.
The Liberal National Party's Teresa Gambaro, a former Howard government MP, saw her lead grow from 998 votes on Saturday morning to 1,630 votes by late afternoon.
With more than 51 per cent of the two-candidate preferred vote, she is tipped to end Labor MP Arch Bevis' two decade hold on the inner-city electorate.
This scenario would leave Labor and the coalition with 72 seats each in the House of Representatives - less than the 76 needed for a majority.
That leaves four independents, a maverick National MP and a Greens MP deciding who will form the next government.
