The city's councillors will decide the mayor and deputy mayor for the fifth year of this extended term after elections, due to take place this weekend, were postponed in response to the coronavirus pandemic.

Wagga councillor Tim Koschel intends to put his name forward for the position of deputy mayor, but said he will not support the return of Councillor Conkey as mayor.

"The mayor is our leader and he's been there for four years and we are still not an unified group and struggle to work together and a change is needed," he said.

Cr Koschel said the current deputy mayor Dallas Tout will have his vote if he did choose to step up the ranks, believing he would be "a fair, equitable and independent".

Cr Conkey will once again put his hand up for the top job at the September 28 meeting. He said only time will reveal who else will put their name in the race.

"There is some talent within the council and majority of councillors are showing great leadership with COVID-19," he said.

Cr Tout is "happy with the status quo" intending to stand for deputy mayor again at this stage. However, he said anything could happen in the next few weeks.

Meanwhile, Cr Paul Funnell does not intend to stand for mayor.

However, he said his vote will go to "anyone who had a backbone, would show leadership and not be conflicted in any way".

In Cr Funnell's opinion, the only councillors who fulfilled his criteria for what is required of a mayor were himself, Cr Koschel and Yvonne Braid.

Cr Braid said she was "pretty busy" at the moment and does not intend to step into any leadership role.

Cr Dan Hayes said this fifth term of council is "an unusual circumstance" and has decided to stay with the councillors holding the current leadership positions.

"At the moment I am not seeking any changes for mayor or deputy mayor. I think lets see the final year out of this term," he said.

Likewise, Cr Rod Kendall will not stand for mayor, nor deputy, and intends to support the current councillors in the roles believing stability in the final term of the council was needed.

Cr Kerry Pascoe said he will see what happens in the coming weeks, but will not put his name forward.

Cr Vanessa Keenan was contacted, but did not responded before publication.