Labor MPs are gathering at parliament to discuss a new leader to replace Mr Andrews who will finish in the role at 5pm on Wednesday and relinquish his seat of Mulgrave.
His deputy Jacinta Allan has put her hand up for the top job and is so far the only one to do so publicly.
"There's caucus meeting this morning, I'm looking forward to joining the caucus with my colleagues and letting the usual caucus process run its course," she told reporters as she walked into Victorian parliament.
When asked if she had the support of her Labor colleagues, Ms Allan said she would respect them and let the usual process run its course.
Ms Allan is from the socialist left faction like Mr Andrews but Public Transport Minister Ben Carroll from the party's right is also considered a possible contender.
If successful, Ms Allan would be the state's first female premier since Joan Kirner stepped down in 1992.
The party will meet at midday to discuss the leadership.
Rules stipulate nominations for leadership have to be open for three days but it's uncertain if they will be followed if there is only one nomination.
Attorney-General Jaclyn Symes, who is from the right faction, told reporters she expected Ms Allan would run unopposed and believed a new premier would be chosen on Wednesday regardless.
Ms Symes also ruled herself out of the running for deputy and said she would wait to find out exactly who was running before backing a candidate.
Treasurer Tim Pallas arrived at parliament and did not rule out a tilt for the deputy role.
"I'm still consulting with my colleagues about that and of course, it's important to see who the leader is and that person get the opportunity to pick the person they want to be deputy," he told reporters.
Mr Pallas said it was up to the caucus to determine whether the three days needs to be stuck to.
Former federal opposition leader Bill Shorten said if the Bendigo East MP was successful she would ensure all Victorians were represented on Spring Street.
"She's a very highly successful, accomplished woman leader in her own right," Mr Shorten told ABC Radio National.
"She comes from the regions, she's a very experienced politician."
Mr Andrews announced his decision to step down at a press conference on Tuesday.
The outgoing premier cited thoughts about life after the top job, hinting he could work in the private sector after taking time off.
Mr Andrews became premier in November 2014, booting out a first-term Liberal government, and led Labor to victories in 2018 and last year.
During the 2022 campaign and the months after, he repeatedly said he would stay for the full four-year term.
His change of heart was a recent decision, he said.
Prime Minister Anthony Albanese told ABC Radio Melbourne on Wednesday Mr Andrews had been a strong leader and passionate Victorian.
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