John Barilaro wants a clear run if he stands, with no Liberal rival

Mr Barilaro, currently deputy premier and Nationals leader in NSW, is considering the move over the weekend. He said the Coalition's failure in Gilmore showed the danger of three-cornered contests, and if party research showed he was the best candidate, both parties should get behind him.

"The truth here is this is going to be a tough seat. It's the bellwether seat and no party owns the seat," he said. "If the Prime Minister wants to bolster his numbers in the parliament the best way forward would be a coalition unity ticket - one candidate taking on the Labor Party."

The Nationals won just 7 per cent of the vote in last year's election in the seat, with the Liberal candidate, truffle farmer Fiona Kotvojs, winning 37 per cent, and Mr Kelly 39 per cent for Labor.

But Mr Barilaro said he had won 52 per cent of the first preference vote last year in his state seat, and he insisted people vote for people more than parties.

Mr Barilaro is considered a national leadership contender, and current leader Michael McCormack gave a less than enthusiastic endorsement of him on Thursday, saying if he decided to put up his hand he had to get through preselection first and then the by-election, which would not be easy, with 100 years of history counting against governments winning by-elections.

"History has a habit of repeating itself," Mr McCormack said.

While Mr Barilaro was a good local candidate, others might also want to stand, he said.

Bega Mayor and Labor frontrunner Kristy McBain did not respond to calls on Thursday. Nor did possible Liberal candidates Senator Jim Molan and state MP Andrew Constance.

Asked about federal leadership ambitions, Mr Barilaro said he brought considerable experience to the federal party room as leader of the NSW Nationals and deputy premier "and if there's an opportunity for me to serve the Prime Minister in any capacity I'm always happy to do that".

But he expected to be a backbencher for some time - "and that's not a bad thing. You start your apprenticeship all over again."

Former Liberal leader and Australian National University professorial fellow John Hewson said Eden-Monaro jealousy guarded its local members, and both Mr Constance and Mr Barilaro had local popularity and profile.

"At this stage, you'd say there's an outside chance against the trend that the government might win," he said.

ABC election analyst Antony Green said everything was working against Labor except the bushfires. The biggest issue for Labor was the loss of Mr Kelly's personal vote in a seat where the margin was small.

"Absolutely everything about the contest says Labor will lose votes because Kelly's not the candidate, and the Nationals have a very high profile and popular candidate. So just those factors mean Labor's got some difficulty trying to hold the seat. The next question is do the bushfire and coronavirus have some impact, and that's impossible to measure."

But ANU politics professor John Warhust said Labor had a good shot at holding the seat with the right candidate in what would be a "neck and neck contest".