The state Labor leader refused to resign after a cross-faction delegation informed her she had lost majority support of party MPs, paving the way for a leadership spill on Tuesday.
In a letter to the party's state secretary on Monday morning, Ms Allan signalled her intention to nominate if it went to an internal vote.
Deputy Premier Ben Carroll, from the party's smaller right faction, laid down the gauntlet after confirming he would throw his hat in the ring.
In a post to social media, Mr Carroll said his colleagues had asked him to stand after informing him the premier had lost the support of the caucus.
"This decision is not easy, but the stakes at the upcoming election are simply too high," he wrote.
If a leadership spill is successful and there are multiple nominations, Victorian Labor faces a minimum 29-day process to elect a new premier, eating away at precious campaign time before a state election in November.
"That's a long time to have the leadership uncertain this close to an election," psephologist Kevin Bonham told AAP.
"We've seen very few of these member ballots actually happen and when they do happen, it's normally straight after an election loss when nobody really minds the timing."
A leadership contest would require caucus and rank-and-file Labor members to vote for their preferred leader, threatening to hamstring the party as it vies for a historic fourth successive term in government.
During that period, Labor would need to elect a caretaker premier who was not a candidate in the vote.
"If they actually have a member ballot, I think it will be very, very bad," Mr Bonham said.
"They will be smashed ... it's just so much ammunition for opposition parties."
Fresh Newspoll figures published by The Australian on Monday indicate support for Labor continues to deteriorate, with Ms Allan's party trailing the Victorian coalition on a two-party-preferred basis 52 per cent to 48 per cent.
More than 70 per cent of the 1035 voters polled from July 23 to 26 said they were dissatisfied with Ms Allan, with Liberal leader Jess Wilson preferred premier by a comfortable margin.
The coalition was leading the primary vote on 31 per cent, followed by Labor (28 per cent) and One Nation (19 per cent).
Despite Ms Wilson having the edge in the polls, a Labor majority or minority at the November election was "absolutely plausible", Redbridge pollster and former Liberal strategist Tony Barry said.
"Labor has got a significant challenge to hold onto government, but not an impossible one," Mr Barry said.
"A lot of it will come down to the campaign and Labor's ability to sandbag those 12 seats between government and opposition.
"It could be anything from a Labor annihilation to a Labor majority."
The premier withstood leadership rumblings in June after poor polling pointed to a likely electoral defeat and her low popularity rating.
Mr Carroll publicly ruled out a challenge at the time, throwing his weight behind the premier.
Standing beside Ms Allan, the deputy premier denied he was coming for her job or that he would ask her to stand aside.
"I can look you in the eye and I can say that, premier," he told reporters at the time.
Attorney-General Sonya Kilkenny, a close ally of Ms Allan, shrugged off the leadership speculation as gossip on Sunday.
"She has my full support, and this idle gossip doesn't help Victorians," she said.
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