After a bruising week where Ms Ley promised to scrap Australia's climate targets if she were to win government, a newspaper report suggested her disillusioned moderate colleagues could support a rival bid for the leadership by Mr Hastie.
The Western Australian MP has made no secret of his desire to take over the Liberal Party at some point, but conservatives have said there were no immediate plans to mount a challenge.
On Monday, The Australian reported a growing number of moderate Liberals had pulled their support for Ms Ley and would likely back Mr Hastie if a vote were held this week.
Members of the faction disputed that publicly, while some privately conceded a small handful of moderates may be seriously considering the switch.
"Media reports this morning about the moderates are incorrect," leading moderates Anne Ruston and Maria Kovacic said in a joint statement.
"We, along with an overwhelming majority of our moderate colleagues, continue to strongly support Sussan's leadership.
"This matter was resolved in the party room six months ago and Sussan will lead us strongly to the next election," the pair said.
Ms Ley is also a moderate and previously expressed support for the nation's climate targets.
Party members widely viewed Ms Ley's decision to abandon net zero emissions by 2050 as a major concession to the party's conservative factions and the Nationals.
Right-wingers, including Mr Hastie, are now plotting a similar internal campaign on migration policy.
Confronted during a radio interview with a compilation of talkback callers who said they wanted Mr Hastie to take the reins, Ms Ley said people were entitled to their views but she was focused on policy outcomes.
"I'm not here for a sense of ego about me," she told 2GB on Monday.
Internal angst was further heightened by a new Redbridge/Accent Research poll which showed a five-point fall in support for the coalition, to a record low primary vote of 24 per cent.
Just 10 per cent of voters ranked Ms Ley as their preferred prime minister, compared to 40 per cent for Anthony Albanese.
