Tasmania's Liberal Deputy Premier Jeremy Rockliff is reportedly keen to take on the island state's job, following the sudden resignation of Premier Peter Gutwein.
Mr Gutwein announced on Monday he was quitting politics after two years in the role, citing a draining workload during the COVID-19 pandemic.
State Liberal MPs will decide his replacement at a partyroom meeting, which is expected to be held on Friday.
No one has publicly declared an interest in running for premier, but several media outlets report Liberal sources have said Mr Rockliff wants to take up the job.
His office has been contacted for comment.
Mr Rockliff, who holds the health portfolio and several others, has been deputy since the Liberals came to power in 2014.
Federal Tasmanian Liberal MP Bridget Archer, a close friend of Mr Gutwein, has indicated she would not be surprised to see Mr Rockliff put his hand up.
State Greens leader Cassy O'Connor said she would like to see Mr Rockliff step up.
"He's kind and he's decent and intelligent. He's always, I think, put the public interest first," she told reporters on Tuesday.
Mr Gutwein was elected unopposed as premier by the Liberal Party in January 2020 after Will Hodgman's shock decision to depart mid-term.
Mr Rockliff, considered one of the more moderate state Liberals, did not throw his hat in the ring at that point, running on a ticket as Mr Gutwein's deputy.
Infrastructure Minister Michael Ferguson was in contention for the job with Attorney-General Elise Archer as deputy, but the pair pulled out before a partyroom vote.
The Liberals will also need to appoint a new treasurer to follow in Mr Gutwein's shoes and re-allocate his tourism and climate change portfolios.
The party has already been forced into two cabinet shuffles this year.
Sarah Courtney quit politics in early February while education minister after being criticised over the timing of a holiday to France.
Upper house member Jane Howlett left cabinet in late February following the death of her brother.
Mr Gutwein, a father of two, said he resigned to spend more time with his family after 20 years in politics.
The decision came less than a year after he led the Liberals to a record third-straight election victory.
"What I've found after the last two years especially, is I have nothing left in the tank to give," he said in Launceston.
A recount will be held to determine Mr Gutwein's replacement in the state electorate of Bass.
Parliament, scheduled to sit next week, has been prorogued until after Easter.
State Labor Opposition Leader Rebecca White said the Liberals have "descended into absolute chaos".
"This is a government that has imploded and is characterised by disarray with a revolving door of members walking away when they promised Tasmanians leadership," she said.
