Ms Allan is so far the only candidate to come forward before a meeting of Labor's caucus at noon on Wednesday.
"I will be putting myself forward to lead our party & continue the extraordinary work of our Labor government," Ms Allan posted to X, formally known as Twitter.
No other challengers have emerged but public transport minister Ben Carroll has been touted as a possible alternative and if he runs it would force a leadership ballot.
Mr Andrews said he would not interfere by making phone calls or lobbying for candidates.
But he also pointed out that two thirds of his cabinet are women, saying this had led to better policies and government.
"I'm not here to speculate on who (the next leader) might be and to give you my form guide or any of that," he told reporters.
"It's a matter for the colleagues and I am deeply respectful of that process."
Ms Allan attended the premier's resignation press conference in Melbourne on Tuesday and stood behind a media pack along with other members of cabinet.
She took over as deputy and presumed successor in June 2022.
In addition to her role as deputy premier, the Bendigo East MP is also minister for transport infrastructure and the suburban rail loop project.
She was also charged with delivering the now-cancelled 2026 Commonwealth Games until the portfolio was abolished.
Ms Allan joined parliament in 1999 and is a member of the Socialist Left faction, like Mr Andrews.
Her election last year bucked longstanding Labor convention that the left and right factions install one of their own as either the premier or deputy premier.
If elected leader, Ms Allan would become the state's second female premier, with Joan Kirner serving in the top role from 1990 to 1992.
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