Mr Constance on Wednesday unexpectedly announced his withdrawal from the contest just 24 hours after he'd put his hand up.

"You read the paper like I did this morning and go 'Nah stuff that'," Mr Constance told the ABC.

"I hadn't signed up to contest federally to be called that type of smear.

"That kind of white-anting doesn't just stop with that front page it goes on and on."

The Daily Telegraph ran images of Mr Constance and Mr Barilaro on its front page on Wednesday with the phrase: "C#?! He called him what?"

Mr Constance said the spat was "disappointing" and "humiliating" but he forgave the deputy premier and they remained mates.

"I've had a gutful of this stuff. I know John didn't mean it, in that discussion I had with him today, but ultimately (who) does this all benefit?"

Mr Constance has been open about his mental health struggles after fleeing his Malua Bay property south of Batemans Bay during this summer's unprecedented bushfires.

The transport minister on Wednesday apologised to people who'd been "confused" by his actions this week.

The state MP for Bega on Tuesday had insisted he wanted to head to Canberra to put several issues on the national agenda - including bushfire recovery and the COVID-19 crisis.

Mr Barilaro revealed on Monday he would not contest the South Coast seat for the Nationals.

Asked about Mr Constance's about-face before Wednesday's ABC interview, Mr Barilaro's office told AAP: "The deputy premier has just learned of this and his position hasn't changed."

After announcing he wouldn't be running, Mr Barilaro launched a scathing attack on Nationals federal leader Michael McCormack, using a text message leaked to Sky News.

The deputy premier told Mr McCormack - the deputy prime minister - he was threatened by the NSW Nationals leader.

"You have failed your team and failed as a leader," Mr Barilaro wrote.

Mr McCormack's deputy, David Littleproud, nevertheless on Wednesday declared Mr Barilaro was a talent who would "add a lot to the diversity of the (federal) National Party party room".

"We'd love to have him," he told Sky News.

Liberal senator Jim Molan revealed on Wednesday he wasn't interested in a potential move to the lower house in Eden-Monaro.

Senator Molan announced he'd wouldn't be nominating for Liberal preselection an hour after Mr Constance's withdrawal.

"It is my belief that the most important contribution I can make to the Morrison government, and to serve the people of NSW who supported me so strongly, is to continue to engage on national security and sovereignty issues in the Senate," he said in a statement.

Senator Molan said his decision was strongly influenced by the fact he is scheduled to have surgery on Thursday for an undisclosed condition from which he expects to make a full recovery.

Eden-Monaro was vacated last week when popular Labor member Mike Kelly retired due to ill-health.

The Liberals' 2019 candidate for the seat, Fiona Kotvojs who lost by 0.9 per cent, is believed to be considering another run. Comment is being sought from Dr Kotvojs.

Former Navy seaman Jerry Nockles and National Farmers' Federation general manager for economics and trade Pru Gordon are also reportedly putting their hands up for preselection. Comment has been sought from both.

Nominations for Liberal Party preselection close on Friday morning.

Bega mayor Kristy McBain has already been selected as Labor's candidate.

Senior Labor frontbencher Chris Bowen on Wednesday said the coalition was focused on internal squabbling rather than the people of Eden-Monaro.

"(They are) focused on personalities, not people, on careers, not community," he told ABC TV.

Australian Associated Press