The Canberra Times understands up to four of the party's 11 MLAs have been open to removing Mr Coe as leader.

Deputy Opposition Leader Nicole Lawder confirmed different "points of view" on the Liberal leadership were aired at a party room meeting on Monday morning, but insisted the opposition was now "united" behind Mr Coe.

Ms Lawder was the only Liberal MLA to publicly address reports that some of her colleagues were canvassing the option of replacing Mr Coe as party leader - possibly with senior moderate Elizabeth Lee.

One Liberal source described the attempted coup as "amateurish".

Ms Lee did not respond to calls from The Canberra Times asking to clarify her position. But she took to Twitter, saying she was committed to winning next year's election under Mr Coe's leadership.

Despite those assurances, speculation about Mr Coe's leadership is likely to loom large over the year's final week of sittings in the ACT Legislative Assembly.

Ms Lawder fronted reporters on Monday to discuss crime in Tuggeranong - but attention quickly turned to rumblings about her party's leadership.

She described the speculation as a "storm in a tea cup", but acknowledged there were "one or two disaffected" people in the Liberal party room.

Mr Coe did not comment on Monday, but he was understood to be buoyed by the level of support he received from colleagues since reports of the potential coup emerged.

It was understood that Mr Coe wasn't surprised by the rumoured challenge, as he has been forced to contend with resistance from a small section of his party room since taking on the leadership in the wake of the 2016 election.

Ms Lawder insisted the Liberals were united behind Mr Coe, even suggesting party unity would be strengthened by the leadership speculation.

She maintained that the opposition could win next October's election with Mr Coe at the helm.

Asked if the Liberals would be better placed to topple Labor with a more moderate leader in charge, Ms Lawder said: "If only I had a crystal ball ... I would be able to answer these questions."

"This is what the party room has decided [to support Mr Coe] and this is the way forward," she said.

"We're not looking back or contemplating our navels. We're looking forward, the election is less than 12 months away - that's entirely the whole team's focus."

A senior party source said it was a "bit of a stretch" to suggest that disaffected MLAs were "doing the numbers" ahead of a serious challenge to Mr Coe's leadership.

Instead, party members had simply been "having robust discussions about the best way forward", the source said.

Outgoing ACT Labor secretary Matt Byrne said Ms Lee's failure to hose down the speculation until more than 24 hours after the story surfaced implied a change in leadership was being seriously considered within the party.

"The Canberra Liberals have finally joined the rest of Canberra and realised having one of the most conservative politicians as leader is toxic for your vote," Mr Byrne said.

"But I don't think it really matters who their leader is, it's controlled by the hard right."

He disputed Ms Lee's credentials as a moderate, claiming she was a climate sceptic.

"I think the only thing she's ever come out in favour of is marriage equality," Mr Byrne said.

Rumblings about Mr Coe's leadership come as the Canberra Liberals prepare to preselect the remaining 15 candidates for their 2020 election team.

Aside from the retiring Vicki Dunne, all of the Liberals' sitting MLAs have already been endorsed to contest the October 2020 ballot.

Branch members in each of the five electorates will meet this week to select non-incumbents, although contested ballots will only be needed for two seats - the Belconnen-based seat of Ginninderra and the electorate of Brindabella, in Canberra's south.