Two members of Malcolm Turnbull's extended family are being named as potential contenders in a race for a NSW seat in the Senate, while Victorian Liberal Sarah Henderson is the favourite for a similar contest in Victoria.
Mr Turnbull's son-in-law, James Brown, was named by several Liberals on Monday as an option for the key position in the upper house, to be made vacant later this year following the appointment of Arthur Sinodinos as Australia’s next ambassador in Washington.
But Mr Turnbull's brother-in-law, Michael Hughes, is also being put forward by Liberals as a possible choice because of his long years of service to the party, including as treasurer of its NSW division.
Other contenders for the NSW seat include Dallas McInerney, the chief executive of Catholic Schools NSW, Warren Mundine, who ran for the marginal seat of Gilmore on the state's south coast at the May 18 election, and Richard Shields, one of the candidates who came close to gaining the pre-selection for Mr Turnbull's former seat of Wentworth in Sydney's eastern suburbs last year.
With a highly contested seat up for grabs, party members also said the field could include heart surgeon and professor Michael Feneley and the former mayor of Liverpool, Ned Mannoun.
The selection of a new senator is at an early stage, given Senator Sinodinos is not expected to be formally appointed to Washington until much later in the year, and there is time for many others to put themselves forward and others to withdraw before any formal preselection.
The list of potential candidates also includes one woman, Mary-Lou Jarvis, who is the president of the Liberal Women's Council and a vice-president of the party's state division.
Captain Brown, who is married to Mr Turnbull's daughter, Daisy, is the president of the NSW RSL and served in the army in Iraq, Afghanistan and the Solomon Islands.
He is an adjunct associate professor at the University of Sydney after working as a research fellow at the Lowy Institute for International Policy and the university's United States Studies Centre.
Mr Hughes, who is the brother of Mr Turnbull's wife, Lucy, is a Sydney stockbroker and businessman who has been involved in the Liberal Party since he was a teenager. He, Lucy and their brother Tom jnr are the children of Tom Hughes, who was a federal Liberal MP for nine years, attorney-general in the government of John Gorton, and later a prominent Sydney barrister.
While there was speculation that former army general Jim Molan might also be a candidate, his fate is yet to be determined by the counting of the votes from the May 18 election, in which he was fourth on the Coalition's Senate ticket.
Senator Molan, whose term expires on June 30 if he is not re-elected, offended some within the Liberal Party by running a “below the line” campaign asking people to give him their votes rather than following the official Coalition ticket.
The Victorian Senate race follows Mr Morrison's announcement that former communications minister Mitch Fifield would take up the position of ambassador to the United Nations in New York later this year.
Senator Fifield and Senator Sinodinos are yet to resign from the upper house but are expected to do so later this year, once their diplomatic posts are officially confirmed.
Ms Henderson, a former assistant minister, last week conceded she had lost the seat of Corangamite at the election but she is highly regarded and is seen as the favourite to replace Senator Fifield.
Others named by Liberals as potential choices for the seat in south-west Victoria include Kate Ashmore, who ran for the seat of Macnamara in Greater Melbourne, and Steve Martin, who ran for the seat of Indi in north-east Victoria at the federal election.