Treasurer Peter Gutwein is said to be maintaining an advantage in the Liberal leadership contest, and there's a chance the ballot could be reduced to a one-horse race.
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A source close to leadership aspirant Michael Ferguson conceded on Sunday that Mr Gutwein had "his nose in front".
The Parliamentary Liberal Party will vote at midday on Monday to decide who will lead them into the future.
It comes after Premier Will Hodgman made the shock announcement last Tuesday that he would be resigning.
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Following a two-day period of uncertainty around who in the Liberal Party would put their hand up for the leadership, Infrastructure Minister Mr Ferguson and Mr Gutwein released statements on Thursday confirming that they would be contending for the top job.
Mr Ferguson is running on a joint ticket with Attorney-General Elise Archer, who hopes to be deputy premier, while Mr Gutwein is running with current Deputy Premier Jeremy Rockliff backing him up.
Mr Hodgman has stated he won't be participating in the vote, even if a tie eventuates and a casting vote could be utilised.
As it stands, 14 PLP members will decide who wins.
The leadership candidates spent the weekend pitching their visions for the state to their PLP colleagues. On Saturday, Mr Gutwein's camp appeared confident it had secured at least eight votes, which would indicate majority support from Liberal parliamentarians.
And there seems to be a prevailing acknowledgment that Mr Gutwein continues to lead the race.
"Gutwein's got his nose in front," a source in Mr Ferguson's camp said.
"There's a reasonable chance there'll be no contest.
"The responsible team approach would be to consider whether a vote is necessary."
A Liberal figure close to the Gutwein camp confirmed that the Treasurer appeared to be holding on to a narrow lead.
"I don't know that there's been a lot of change in the situation, quite frankly," the source said.
"I ... can't see how Ferguson can actually get to eight [votes].
"From what I can see, the best he can hope for would be seven, which would obviously represent a separate set of challenges."
Some observers say there's an outside chance the PLP could return a seven-all result.
If that happens a second ballot will be held and, if still tied, a short break may occur before members reconvene for another ballot.
I ... can't see how Ferguson can actually get to eight [votes].
- A Liberal source
Election analyst Kevin Bonham said he was unaware of tied ballots for leadership occurring in the past but added "that doesn't mean they haven't happened".
"A tied vote is not a good look," Dr Bonham said.
"It will be very close and we're not hearing much noise about how people intend to vote."
Human Services Minister Roger Jaensch told media on Sunday that he'd made his mind up about who he was going to vote for but refused to comment further on his decision.
"Whichever way [the ballot] goes, we'll come out with a great leader and a very unified team around them, like we've had over the last six years in government," he said.
Meanwhile, Labor leader Rebecca White said the contest had exposed fault-lines within the Liberal Party.
"No matter who comes out tomorrow as the Premier of Tasmania, what we do know is that about half their colleagues around the table don't think they're the right person for the job," she said.