I have informed the acting Prime Minister, Mathias Cormann, of this, ' he told reporters.
Assistant Families Minister David Gillespie could put his hand up to replace Joyce amid reports the NSW Nationals MP has indicated to colleagues his willingness to run if he resigns.
When asked if media should expose personal relationships of politicians, he said it should not happen again.
Joyce had spent the past week on "holiday" in Armidale, though he made a number of media appearances, including a candid interview with his partner and former media advisor, Vikki Campion.
Mr Joyce has faced sustained pressure to step down after revelations of his affair with a former staffer became public.
It went from bad to worse for Mr Joyce this week.
"Any allegation of sexual harassment is a serious allegation".
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She added: "Here's to more women on these stages, more women winning awards and more women taking over the world". Following the attack, Ariana staged a One Love Manchester benefit concert to raise money for those affected.
Mr Joyce says the allegation is "spurious and defamatory".
He said allegations of wrongdoing would be referred to police.
"He needs to step down as leader of the National Party, take a step back into the back bench for a time", Andrew Broad a member of parliament from Joyce's National Party told state-owned broadcaster the ABC.
"Barnaby made a shocking error of judgment in having an affair with a young woman working in his office", Mr Turnbull said at the time.
Joyce had resisted calls to resign as leader of the National Party and thus as deputy prime minister since news of his long-running affair with his media adviser, 33-year-old Vikki Campion, broke nearly two weeks ago. However, Joyce has continually asserted his desire to stay on as the party leader and the nation's deputy PM. "As leader of the National Party of Australia in a Coalition government, he is my Deputy Prime Minister", Mr Turnbull said.
"I've been at great pains to stress that I have not, nor has my Party, sought to influence in any way, the deliberations of the National Party, any more than I'd expect the National Party to seek to influence deliberations of the Liberal Party".
However, the Party's federal director Ben Hindmarsh reportedly said in a statement that "all complaints are taken seriously and treated with the strict confidentiality and given due process".