Nominations follow a week that saw Bega MP Andrew Constance backflip on a switch to federal politics following disparaging remarks by Coalition colleague John Barilaro.

On Friday, online bookmaker Sportsbet had Labor's byelection candidate Kristy McBain as favourite to win, which is in contrast to Labor leader Anthony Albanese's claim the Liberal Party is favourite to reclaim the former bellwether seat.

If the Liberal Party were to take the marginal electorate, it would be the first time that a government has won a seat held by the opposition party in a byelection since Kalgoorlie in 1920.

NSW Nationals leader Mr Barilaro had earlier pulled out of a run at the electorate, blaming deputy prime minister Michael McCormack for not backing him, and Mr Constance, who has since been dropped as the government's Leader of the House, for looking into a three-cornered race.

The withdrawal of the pair has avoided possible state byelections in both Bega and on the Monaro.

On Friday, Mr Constance was back in his electorate overseeing the delivery of shipping container pods for bushfire-affected residents funded by billionaire mining magnate Andrew "Twiggy" Forrest's Minderoo Foundation with help from the state government.

"Locals have been in tears when they get them," Mr Constance posted on social media.

Meanwhile, the Liberal Party is moving ahead with the selection of it's byelection candidate in an attempt to regain the seat's bellwether status.

A Liberal Party spokesperson said on Friday, preselection nominations are now closed and the party is currently "checking that nominations submitted meet constitutional requirements", as political parties attempt to avoid a rerun of the Australian parliamentary eligibility crisis which saw eight senators and seven lower house MPs step down.

"In the circumstance where there are multiple valid nominations, the party will then conduct an electronic plebiscite of local branch members in line with social distancing requirements," the spokesperson said.

"The candidate chosen by our members will then hit the ground campaigning across the Eden-Monaro community."

On Friday, online bookmaker Sportsbet had last year's federal election candidate and Dignams Creek truffle farmer Fiona Kotvojs as odds on favourite to become the Liberal's byelection candidate.

Ms Kotvojs sits ahead of former Peter Hendy staffer Jerry Nockles, who withdrew from their previous preselection battle due to family reasons, and National Farmers' Federation general manager of trade and economics Prudence Gordon.

Ms Gordon has previously worked at the Australian Embassy in Washington DC, and for the department of foreign affairs, where she focused on trade with China.

Self-professed 'Menzies Liberal' and ex-Army engineer Nigel Catchlove sits behind them as a rank outsider.

Both Mr Catchlove and World Vision Australia and former Hoover Institution visiting scholar Dr Nockles had hopes of contending the 2019 election, which saw Ms Kotvojs narrowly defeated by now-retired Eden-Monaro MP Mike Kelly.

With the Australian Electoral Commission's logistics for the byelection still not known, due to the ongoing COVID-19 mass gathering restrictions, the Liberal Party said its campaign will need to adapt to the current health crisis.

"While our approach to campaigning has changed because of the COVID-19 pandemic outbreak, we will still be reaching out and engaging with communities right across Eden-Monaro," the party spokesperson said.

"The Morrison government remains focused on keeping Australians safe and rebuilding - rebuilding an economy devastated by coronavirus and rebuilding local communities devastated by the fires."

It is understood the party may announce its byelection candidate as early as next week.