"[Gillard] has already shown a new assertiveness and the reshuffle should be part of that," Regional Minister Simon Crean said.
Front-runners for the Foreign Ministry include Rudd's predecessor in the job, Defence Minister Stephen Smith, Crean, and Trade Minister Craig Emerson, at present acting in the position.
Gillard's room to move has been expanded by the surprise resignation on Monday of former Assistant Treasurer and Sports Minister Mark Arbib, whose decision to quit politics has also created a vacancy for a new Labor Senator from New South Wales.
There is no indication yet of who will replace Arbib in the Upper House.
Former national Labor Party president Warren Mundine is a potential candidate, but former NSW Premiers Bob Carr and Kristina Keneally rejected reports that they were in the running.
Gillard has refused comment on the membership of her new Cabinet.
"I'm not going to be speculating on [the reshuffle] before I announce it," she told ABC radio.
"I will judge my team on ... merit and the capacity to take the fight up to the other side of politics."
That fight has already begun in Parliament, where the Opposition has been trying to link Labor policy with the aftermath of the leadership contest, spurred by former Liberal Deputy Prime Minister Peter Costello, himself frustrated in a bid to take the top job from John Howard, the man Rudd defeated in 2007.
"While [Rudd] has breath he will be angling for the leadership," Costello wrote in the Age.
"Even if he wanted to be, he cannot be loyal to another leader.
"He will brood and he will fester."
In Parliament Gillard rebutted an attack on her failed plan to process asylum seekers in Malaysia - and later also Nauru - accusing the Opposition of risking lives by blocking a policy it had previously supported, and acting against the national interest.
She will also increasingly have to deflect attacks on her carbon and mining taxes, both areas in which Opposition Leader Tony Abbott has been able to score telling points.
But on ABC Radio Emerson said Gillard would not shirk important reforms, most of which have been previously overshadowed by the leadership crisis.
"These are big reforms, not very popular reforms, and now the task of explaining the benefits is before us," he said.
"The onus will shift on to Tony Abbott after July 1 in explaining why he would repeal the carbon tax, why he would repeal the mining tax ... and I'm certainly looking forward to that because I don't think he'll have any plausible explanation for either."
The carbon tax begins in July, providing revenue to fund new payments, benefit increases and future tax cuts to compensate for predicted power price rises which, after they take effect, are expected to blunt much of Abbott's attack.
Gillard's priorities now include a national disability insurance scheme, a federal-state skills training programme, new investment in the ailing car industry, and an overhaul of education funding.
There will be more hard decisions: possible increases in personal nursing care costs in an aged care reform package, the continuing debate over the management of the ailing Murray-Darling Basin, and growing demands for a A$10 billion ($13.7 billion) universal dental care scheme.
