Bridget McKenzie is still weighing up a move to the lower house, and with it potential leadership of the Nationals, as the besieged Coalition partner struggles to move on from its latest MP sex scandal.

The Nationals leader, Michael McCormack, said McKenzie would have his “full support” if she chose to step away from the Senate and run in the electorate of Mallee, following Andrew Broad’s announcement he would be stepping down at the next election.

McKenzie had considered running in Indi, held by the independent MP Cathy McGowan, but Mallee, with it’s almost 20% margin, is considered a much safer bet for the Nationals deputy.

McKenzie’s potential move to Mallee was floated almost immediately after Broad announced he would not be recontesting the next election.

“If Bridget McKenzie wants to run in the seat of Mallee, she’ll have my full support,” McCormack said on Thursday.

“She’s an outstanding colleague and outstanding deputy leader and outstanding senator for Victoria.

Asked directly, McKenzie did not rule out a tilt at a shift to the lower house. “Three years ago I ran to be senator for the great state of Victoria for six years,” she said.

“That’s the job application I put in to Victorians. That is the role that I’m fulfilling now. I have been blessed to have been elected the deputy leader a year ago.

“I supported the previous leader. I’m backing up our current leader who is going to lead us to the next election and that’s what I’m focused on.

“… I love that question because it sort of like, “Do you have any leadership ambitions.” Well I ran for the deputy leadership and my role is to back the leader which I always do.”

The blue ribbon seat came into play after Broad, who had served as a junior minister in the Morrison government, was alleged to have attempted to start a relationship with a woman from a ‘sugar baby’ dating website.

The woman, identified only as Amy, told New Idea magazine Broad had arranged to meet her in Hong Kong in September, making public a series of sexually charged messages the married MP had sent her, in an exchange which has been dubbed ‘fifty shades of g’day’ on social media.

The former leader Barnaby Joyce, who has also not given up his own leadership ambitions, told the Australian he was aware women had made allegations of sexual indiscretions against Broad while he was leader, but “no complaints were ever made, so there was nothing to pursue because you can’t go chasing rumours”.

That statement contradicted McCormack’s statement that he was unaware of any other issues surrounding Broad’s history with women, until the Herald Sun published the claims this week.

The Nationals’ year was bookended by sex scandals, starting with Joyce’s admission he’d had an affair with one of his staffers, and ending with Broad. Internal tensions between the Liberals and Nationals bubbled away in-between.

The LNP senator Barry O’Sullivan was also named in the Senate during a debate on standards for what other senators said were inappropriate comments directed towards women, while last week, his staffer was stood down, on pay, for an abusive text message he sent a female journalist.

Earlier in the week, McCormack attempted to bat away claims the party had an issue with women by noting both women in the 22-strong Nationals party room were in the ministry.

Standing next to McCormack, McKenzie would not weigh in on the issue, beyond citing a statement she made in the wake of the Broad affair.

“Look, I think, as I have said publicly, in my public statement, it’s been disappointing and not reflective of the National party members and senators, more broadly, and indeed our membership expectations or the broader community.

“So I think Andrew Broad made the right decision to resign from the ministry and to retire at the next election and to focus on his family.”