Former Prime Minister Gordon Brown has ruled himself out of the Scottish Labour leadership contest, the BBC understands.
He is the latest in a number of key figures to say they will not stand for the post vacated by Johann Lamont.
Earlier, MSPs Kezia Dugdale and Jenny Marra ruled themselves out.
And the party's acting leader, MP Anas Sarwar said he wanted to concentrate on General Election planning.
Scottish Labour's health spokesman, MSP Neil Findlay - who is seen as a potential candidate - had urged Mr Brown to take over the reins.
But a source close to the Fife MP told the BBC: "For the past four years and on every occasion that he has been asked, Mr Brown has made it clear that he is not returning to frontline politics. That position has not changed."
At Westminster, it is thought that the shadow international development secretary, Jim Murphy, is the most likely candidate.
Labour MSPs were to meet in Glasgow at lunchtime to discuss Ms Lamont's departure after nearly three years as leader. Labour MPs will later meet in Westminster to discuss the party's future north of the border.
The party has confirmed that MSP Jackie Baillie will speak for Labour at first minister's questions this week, although it has not said if this will continue to be the arrangement until a new leader is chosen.
A new Scottish leader, who could be an MP, MSP or MEP, is due to be in place by 13 December.
Speculation is mounting about who might stand.
How is the new leader elected?
- Strathclyde University politics Professor John Curtice explains that an electoral college will help produce the next Scottish Labour Party leader.
- He says there are in effect three separate ballots which are each worth a third of the vote.
- One third comes from the Labour parliamentarians at Strasbourg, Holyrood and Westminster.
- One third comes from members of the party in Scotland
- And one third comes from members of affiliated trade unions and affiliated societies
Scottish Labour leadership
Who gets a vote?
1. MPs, MSPs and MEPs
2 Party members in Scotland
3. Trade union members in Scotland
Meanwhile, shadow chancellor Ed Balls rejected Ms Lamont's claim that the UK party treats Scotland like a "branch office".
In her resignation letter, the outgoing leader senior said members of the party had "questioned" her place and that she was taking herself "out of the equation" so it could decide the best way forward.
In an earlier interview with the Daily Record, Ms Lamont branded some of her Westminster colleagues as "dinosaurs".
But Mr Balls insisted: "We're a UK party but have a really vibrant and dynamic Labour party in Scotland."
Voters wanted a leader who would be "a strong voice for Scotland", he added.
Labour MP Katy Clark said the Scottish party needed "a significant move to the left".
She told the BBC's Daily Politics: "The Scottish Labour Party already has a different policy, for example, on Trident.
"We vote against Trident at our conferences and we can't ignore that because that's where the Scottish people are, and in every opinion poll since the 1950s the Scottish people said they don't want nuclear weapons."
However, former Labour Home Secretary David Blunkett told the programme: "We can't have a different policy on Trident in Scotland as we have in England and Wales because it's a defence policy."
Mr Blunkett also dismissed the notion that Gordon Brown would want to lead Scottish Labour.
The group Labour for Scotland, which includes former MSPs Frank McAveety and Pauline McNeill, has called for the Scottish party to become fully autonomous from the London leadership and back full devolution of income tax and welfare.
The group is backed by MSPs Michael McMahon and Cara Hilton.
Meanwhile, Ms Baillie has denied there were factions of Labour MSPs and MPs within the party, and insisted they were "joined at the hip" in doing the best they could.
She told BBC Radio Scotland's Good Morning Scotland programme that it was natural for there to "always be" a debate between MPs and MSPs, but she denied there had been the levels of interference stated by Ms Lamont.
Ms Baillie said: "Whether you are an MP or MSP in Scotland you are representing constituents in Scotland.
"It doesn't matter what chamber you are in, you are absolutely joined at the hip in wanting the best that we can."
Ms Baillie has ruled herself out of the contest, saying she would rather play a "supporting role" than be leader.
She told presenter Gary Robertson: "I believe we should have a very open contest and I look forward to a number of different names emerging, be they MPs, MSPs or indeed MEPs, who are entitled to stand as well.
"But I think it would be really helpful to have a debate in the party where we have quite a lengthy nominations process that tries to balance a speedy transition, but yet a clear desire for the members to have their voice heard.
"I think you will see a number of people coming forward in the coming days and I look forward to that very much."