While Bishop did not explicitly endorse Rudd's candidacy, her comments came after Liberal National Party (LNP) members of parliament said the former prime minister was not qualified for the role, Xinhua news agency reported.
"I believe that as the other candidates are former leaders, former prime ministers, former foreign ministers of their country, then he is qualified to be a candidate," Bishop said.
Prime Minister Malcolm Turnbull's cabinet will meet on Thursday to debate whether the incumbent government will officially nominate Rudd for the post. Without that support, Rudd could not be considered for the role.
At least two high-profile ministers have cast doubt over Rudd's qualifications for the role, with Cabinet Secretary Arthur Sinodinos saying that members of the centre-right LNP would be hesitant to support the former prime minister.
"I'm not spilling any secrets to say there would be a lot of people on our side of politics to say they have reservations about supporting Kevin," Sinodinos said on Monday night.
"The politics of that era are still pretty raw and the idea that he could be on the world stage seeking to overshadow Australia in other ways does grate with some of my colleagues."
An Essential poll taken in April found that twice as many Australians supported former New Zealand Prime Minister Helen Clark for the UN top job over Rudd.
Rudd served as Australia's Prime Minister twice: from 2007 to 2010, then from June 2013 until his centre-left Australian Labour Party (ALP) lost the election in September of the same year.
The first straw poll of the 12 candidates for the vacant UN position resulted in a clear win for former Portuguese Prime Minister Antonio Guterres.
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