The leader of Australia's Opposition Australian Labor Party (ALP), Bill Shorten, has moved to interrupt the government's plan to appoint a new governor-general (GG) before the next election.

In a letter to new Prime Minister Scott Morrison on Monday, Shorten asked him to extend current GG Peter Cosgrove's five-year term until after the election, allowing the victorious party to make the key appointment.

The letter came amid speculation that Morrison would seek to appoint Julie Bishop, the former minister for foreign affairs and deputy leader of Morrison's Liberal Party between 2007 and 2018, as GG when Cosgrove's term expires in March 2019.

The governor-general of Australia is the representative of Australia's monarch, currently Queen Elizabeth II, in Canberra.

The office has the power to dismiss the government, call elections, appoint ministers and judges and give royal assent to legislation passed by parliament although the GG almost always acts on the advice of the sitting prime minister.

Shorten asked Morrison to extend the term until September 2019, a move that would allow Shorten to appoint the next GG if he wins the federal election, which is expected to be held in May 2019.

"Given that a general election must be held in or before May of next year, an extension to his term would allow an incoming prime minister to nominate to Her Majesty Queen Elizabeth II an appropriate successor and new governor-general following the next election," said Shorten's letter, published by News Corp Australia on Tuesday.

"Such an extension is within convention and would be supported by the Opposition.

"I look forward to your prompt response on this matter."

Bishop on Sunday announced her resignation as the minister for foreign affairs after she was defeated in a ballot on the leadership of the Liberal Party by Morrison on Friday.

She has not confirmed that she desires to be the next GG but it has been reported that she will resign from parliament at the next election.