Bill Shorten wants the winner of the next election to nominate a new governor-general in the wake of speculation about Julie Bishop’s future.

Following Ms Bishop stepping down as foreign minister on Sunday, reports suggest she could succeed Sir Peter Cosgrove when his commission ends in March.

But the Labor leader has taken the first step to shut down any potential aspirations for Ms Bishop and the Liberal Party, proposing a six-month extension to Sir Peter’s term.

Mr Shorten has penned a letter to new Prime Minister Scott Morrison, asking him to extend Sir Peter’s commission until September 2019, taking it beyond the likely May 2019 federal election date.

The future of former foreign minister Julie Bishop is open to speculation. Photo: Getty

He believes the move would allow the “incoming prime minister” to nominate “an appropriate successor” after the election.

Sir Peter has served as governor-general since March 2014, following on from Dame Quentin Bryce’s near six-year stint.

Australian Republic Movement director Michael Cooney said the next governor-general should be at least in part chosen by the public.

“Things need to change in Parliament House and it starts with the attitudes and behaviours of the most senior people,” Mr Cooney said.

“Choosing the governor-general should never again be a personal pick of the prime minister.”

-AAP