Education Minister Jack McConnell is the sole nominee for the party's top job after Henry McLeish's surprise resignation last week.
A meeting of MSPs and Labour's executive committee has been called at the party's headquarters in Glasgow on Saturday morning to consider his candidature.
If Mr McConnell receives more than 50% of the votes in the "affirmative ballot" he will be installed as Labour's new leader - and first minister in waiting.
He is then expected to hold talks with Labour's Liberal Democrat coalition partners to ensure their support in the Scottish Parliament vote to choose the successor to Mr McLeish.
Liberal Democrat MSPs have warned that their endorsement of Mr McConnell should not be taken for granted.
Backbencher Mike Rumbles said he would insist on moves towards proportional representation (PR) in council elections as the price of his support.
He said: "One of the questions I am going to ask him when he comes to the group meeting as Labour leader is what his intentions are about reforming local government.
"There's no automatic anointment of Jack McConnell as first minister. He will have to persuade me that it's the right thing for me to do to vote for him.
"Having said that, I expect him to be able to confirm my expectations about PR for local government."
Private life
Mr McConnell and his wife Bridget faced the media on Tuesday to confirm that he had an affair during his time as the general secretary of the Scottish Labour Party during the 1990s.
The confession was designed to stem innuendo about his private life in the press, but it will be some days before it is clear if the tactic has worked.
Labour cancelled plans to send out more than 400,000 voting slips for the leadership contest.
Instead, the party's 55 MSPs and the 29 members of its Scottish executive committee will vote on Saturday to affirm Mr McConnell as the new Scottish Labour leader.
The move has been criticised by opposition parties who said it amounts to nothing more than a coronation and that Mr McConnell has no proof of a mandate.
It was understood that none of the Scottish Cabinet had nominated Mr McConnell.
Mr McConnell's energies will now be focused on Liberal Democrats.
With their support, Mr McConnell could be formally installed as the new first minister by the end of next week.
Meanwhile, Scottish Secretary Helen Liddell has sought to defend the record of devolution in light of the events which led to the resignation of Mr McLeish as first minister last week.
Mrs Liddell told BBC Scotland ahead of a meeting of the right-wing think tank, the Social Market Foundation, that both the parliament and Scottish Executive have demonstrated maturity over recent events.
She also said that during Mr McLeish's leadership the devolved institutions grew in stature.