Following the departure of two veterans of the front bench, Anthony Albanese will declare his new ministry on Sunday afternoon.

The foundation for a more extensive reshuffle has been set by the resignations of Ministers of Indigenous affairs Linda Burney and Skills Brendan O'Connor from their positions before to their retirements at the next federal election.

Concerns about Clare O'Neil's future in home affairs have led to the likely removal of Immigration Minister Andrew Giles from her position. Murray Watt, a senator from Queensland, has been mentioned as a prospective candidate for promotion, possibly to the position of immigration, skills, or industrial relations.

O'Neil and Giles are anticipated to stay in cabinet even if they are removed from their portfolios.

The focus has shifted to the Senate and who is willing to help share the load because it is believed that the existing ministry is too heavily weighted toward the House of Representatives.

Senator Malarndirri McCarthy is tipped to receive a promotion to the head of the Indigenous affairs portfolio, while her upper house colleague Jenny McAllister is also expected to be handed her first ministry.

The Tasmanian senator Carol Brown announced on Saturday that she will be stepping aside from her assistant transport minister position to focus on her health. With the expected elevation of McCarthy and McAllister and Brown’s resignation, backbenchers are jostling for a promotion to one of the three assistant minister positions which have opened up.

As prime minister, Albanese can appoint assistant ministers, but ministry appointments in Labor are a more complicated affair, with the caucus holding sway over positions.

The reshuffle is not expected to be wide, with Albanese placing emphasis on the “stability” of his government in previous announcements.

In his last day as a minister, O’Connor told the ABC he believed there was a lot of talent among his colleagues but remained tightlipped as to his replacement.

“I think people mention Murray Watt, I think he’s done a great job in agriculture and he and I worked very closely on the skills area,” he said.

“I think there’s a lot of people, though. It’s great to see it looks likely that Malarndirri McCarthy and Jenny McAllister will enter the ministry. They’re assistant ministers now, they both got remarkable energy and talent and I look forward to watching them if that’s the case in the ministry.”

With speculation Tony Burke could be moved into the home affairs portfolio, the shadow minister, James Paterson, said it didn’t matter. The opposition wanted to see the portfolio returned to how previous Coalition government’s had set it up, he said.

“They dismantled the portfolio when they came to office by taking key agencies like the federal police and the intelligence commission out of the portfolio and sent it to the attorney general’s portfolio,” Paterson told Sky News.

“And it’s caused chaos and confusion in national security policy ever since, as Clare O’Neil and Mark Dreyfus engage in serious fights. No matter what the government does, we will continue to have a home affairs portfolio as it was when we were in government. And it’s my intention to seek the restoration of that portfolio to its former glory so … we can have all our operational and policy agencies on national security working together in a seamless way.”

Albanese has announced a press conference for later Sunday afternoon.