'See out full term' Vic MP tells colleague

Victorian MP Jane Garrett should shelve any aspirations she has to be Melbourne Lord Mayor and stick out her parliamentary term, Labor colleague James Merlino says.

Ms Garrett hopes to decide by the end of this week if she will trigger a by-election in her marginal seat of Brunswick and make a tilt for lord mayor after the resignation of Robert Doyle.

"I've got an old fashioned view, unless you're retiring completely from public life, if you're elected by a community, you should honour that commitment and serve a full term," Emergency Services Minister and acting Premier James Merlino told reporters on Monday.

Mr Merlino replaced Ms Garrett when she quit the ministry in mid-2016 after a fallout with Premier Daniel Andrews over the handling of a CFA pay dispute.

A by-election for lord mayor is scheduled for May 12 after Mr Doyle quit amid sexual harassment allegations, which he vehemently denies.

Former City of Melbourne councillor Tessa Sullivan in December claimed sexual misconduct by the then-lord mayor against her and colleague Cathy Oke, sparking an investigation.

"I'm hoping later this week I'll be able to say," Ms Garrett said on 3AW on Sunday.

"Clearly this has come out of the blue because of the very unfortunate circumstances surrounding the town hall so anybody who's thinking of standing has to go through some pretty serious due diligence."

Acting Lord Mayor Arron Wood confirmed last week he would not run, but among other rumoured candidates are Moreland councillor Oscar Yildiz, Property Council of Victoria boss Sally Capp, and AFL Footy Show panellist Sam Newman.