Ms Bryce's daughter Chloe married Mr Shorten in November 2009 and they have a daughter Clementine.
The parliamentary secretary was one of the key factional powerbrokers instrumental in the dumping of former prime minister Kevin Rudd for Julia Gillard in June.
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He has been pegged as having aspirations for the top job himself, with one betting agency making him favourite to lead Labor to the next election.
Another parliamentary secretary, Richard Marles, and Liberal backbencher Paul Fletcher were coy when questioned today about suggestions Ms Bryce should step away from the decision-making process for a new government following Saturday's general election.
Labor will need to show the governor-general it can command a majority on the floor of parliament's lower house in order to win her approval for minority government.
"Far be it from me to give advice to the governor-general," Mr Marles told Sky Television.
A leading ethicist Leslie Cannold has told News Limited newspapers that if Ms Bryce eventually has to decide who to appoint as PM, there could be the appearance of a conflict of interest.
