The Labor Government's majority in the Victorian Parliament could be reduced to the slimmest of margins, with former minister Jane Garrett "considering" quitting for a tilt at the Melbourne lord mayorship.

If Ms Garrett decides to contest the mayoral election, triggered by Robert Doyle's resignation, it would force a by-election in the marginal seat of Brunswick, where the Greens are threatening to topple Labor.

The current margin is just 2.2 per cent and Labor are worried, given the hammering it received in neighbouring Northcote in last November's byelection.

If it loses Brunswick, Labor would hold just 44 seats in the 88-member house, but it could rely on the vote of former caucus member Don Nardella.

Mr Nardella sits in Parliament as an independent after being forced from the Labor Party after an entitlements scandal.

Speaking on ABC Melbourne Radio, Ms Garrett told Jon Faine she was considering the approach and that people, including members of the Government, had encouraged her.

"I've had it put to me now by heaps of people that I should consider it and that's all I'm doing at the moment, considering it," she said.

"With my family, obviously there's a range of matters that have to be looked at, but it's a very important role in this community.

"It's an incredibly important role for Melbourne as a whole and Victoria."

She said the Melbourne mayorship was an attractive prospect.

"Anyone interested in politics and civic life in Victoria thinks the lord mayor is an incredible role but there's a long way to go," she said.

"There's a lot of people involved.

"I love serving the community, I loved being a mayor at Yarra, I love being a member of Parliament, I loved being a minister."

Fractured relationship with Premier

Ms Garrett has not spoken to Premier Daniel Andrews about the move and he said he had not entertained the idea.

Mr Andrews was in Canberra for a meeting with the Prime Minister and other premiers and said he had been focused on other issues.

"I have spent very little time today thinking about who is or who is not the Lord Mayor of Melbourne," he said.

"I think the member for Brunswick has a big job to do looking after the people of Brunswick and I expect she'd remain focused on that," Mr Andrews said.

Her resignation from cabinet in 2016 underlined tensions with Mr Andrews over the CFA dispute.

She tried unsuccessfully to win preselection for an Upper House spot last year, after declaring she would not recontest Brunswick.

That defeat has left her without a seat for the 2018 election.

The potential bid for the mayorship comes amidst a major factional realignment in the Victorian Labor Party, with Ms Garrett's Industrial Left group striking a new arrangement with the Centre Unity grouping of the Right.

Under that deal, a new federal seat would go the Industrial Left and some have suggested it could go to Ms Garrett.