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.

Prime Minister Malcolm Turnbull with his grandson Jack, wife Lucy, daughter Daisy and son-in-law James Brown. Credit:Andrew Meares

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.