Queensland MP Bob Katter and New South Wales MPs Rob Oakeshott and Tony Windsor are thought to have been in discussion on with the Coalition over parliamentary reform commitments.
All three have said they expected to make a decision early this week, with each indicating that decision could be as soon as today.
And on broadband at least, Mr Windsor appeared to back Labor, telling The Sunday Age newspaper's Josh Gordon that the National Broadband Network was the better way forward, labelling the opposition's plan as a "retrograde policy."
After separate briefings last week from the Department of Broadband, Communications and the Digital Economy - at which NBN Co chief executive Mike Quigley is thought to have been present - and from Minister Stephen Conroy, Mr Windsor told The Sunday Age he was convinced "you do it once, you do it right, you do it with fibre."
Mr Windsor also told the ABC that in the long term "fibre is the way to go," but said this didn't mean the Coalition's policy was "a complete dud."
Mr Windsor has been an open supporter of the National Broadband Network scheme during the term of the last Government, in comments and speeches inside and outside of the Parliament.
Mr Oakeshott, from the mid-north coast seat of Lyne, has also been supporter of Labor's broadband plans, while Mr Katter's views have been more difficult to read.
Although broadband infrastructure is clearly an issue, it is by no means clear which way the three independents will lean when it comes to supporting Mr Abbott or Ms Gillard.
Either side needs 76 seats in the Lower House to form government. Two weeks after the election, Mr Abbott has 73 seats (with the inclusion of West Australian Tony Crook), while Labor has 74 seats (with the inclusion of Greens MP Adam Bandt and Tasmanian independent Andrew Wilkie.)