Julie Bishop is yet to decide if she wants to stay on as foreign minister under new Prime Minister Scott Morrison.
But the man who caused the leadership upheaval last week, Peter Dutton, has made it clear he would like to return as home affairs minister.
Mr Morrison, who won the leadership ballot against Mr Dutton after Malcolm Turnbull called a spill on Friday, is weighing up forming a ministry to reunite the Liberal party.
Ms Bishop, who also stood for the leadership but was knocked out in the first round of voting with only 11 votes, has returned to Perth.
"I am going to consider all my options and I am going to focus on running (in the City to Surf)," she told the Sunday Times.
"Once I have considered my options I will make a statement."
Ms Bishop, 62, also stood down as deputy leader of the Liberal party.
Education Minister Simon Birmingham said "the most significant woman in the history of the Liberal Party" deserved to make a decision about her future without external pressure.
"We would love to see Julie continue, but that really is up to Julie," he told the ABC on Sunday.
"We will all respect whatever decision she makes."
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