Wagga councillor Vanessa Keenan said she was weighing up her options ahead of the mayoral election on September 24.
Current mayor Greg Conkey has said he will stand for another term and current deputy mayor Dallas Tout said he would stand again for his current role.
Cr Tim Koschel created the possibility of a ballot for mayor by telling The Daily Advertiser on Tuesday that he was “seriously considering” a run for the top job.
Cr Paul Funnell has not ruled “anything in or out”.
Cr Keenan said after spending two years on council, she was thinking about the future.
“I wouldn’t say no. I’m certainly open to the idea (of running for mayor),” she said.
“I’m conscious that I have been on council for a few years now and have been actively involved, particularity in the strategic discussions, in the city and council.
“I’m also really conscious that, as an active female councillor, that it is something that I should at least consider.”
Cr Dan Hayes, who conceded defeat in his campaign in Wagga’s state byelection on Monday, said he had not had time to think about running for mayor.
Cr Hayes did not reveal a preferred candidate for Wagga’s mayor for 2018-20.
“The great thing about council meetings is that they are live-streamed (on Facebook) and the public can come along on Monday week,” he said.
“I will be pushing for an open vote so the public everyone can see which way councillors vote, based on who actually nominates.
“There is an open and transparent way of voting, which I will be pushing for and everyone can see my vote then.”
Councillors will also have the option of casting their vote via secret ballot rather than a public show of hands during the meeting.
Cr Keenan said if she decided not to run, she would back a councillor with a “proven track record” and who could handle a growing city.
“Now is the time to reflect on what has happened over the past few years and what is still to come,” she said,
“We have a lot of significant projects and events coming up and we need to make sure that we have got someone in the role that has the ability to lead the city and the council through these really important times.”
Cr Keenan said was not sure if Cr Koschel, who was still evaluating how he might balance his private work commitments with being mayor, was the best candidate.
“I’m not sure (Cr) Tim (Koschel) will have the time,” she said.
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