A former Scottish Labour finance minister has called on his party to cut its ties with London and become a fully independent political force.
Andy Kerr said that embattled party leader Jim Murphy could "arguably" remain in post if he backed the radical measure.
However, sole Scottish Labour MP Ian Murray rejected the plan, arguing that he and his UK colleagues should "fight together for equality".
Although Scottish Labour has operational autonomy, it is constitutionally an "accounting unit" of the UK party.
UK Labour pays the salaries of staff north of the border, provides cash transfers, and makes shared services available to the Scottish party.
Candidate selections for Westminster are also a matter for the UK national executive committee.
While Scottish Labour has secured greater autonomy in recent years, Kerr believes last week's drubbing means a bolder solution is now required.
He said: "We need an independent Scottish Labour party which has got a federal structure."
"If Jim can say some of these things then arguably he may stay in post. But my worry is that Jim's a product of the system [that] saw Scotland through the prism of their deep hatred for the SNP."
Andrew McFadyen, a former party adviser, supported the call: "Many Scots were simply not prepared to put their trust in Jim Murphy or the Labour Party after they campaigned alongside the Tories for a No vote during the referendum.
"It is going to be very hard to come back from this defeat. The starting point must be for Scottish Labour to demand its own independence from London and move to create a genuinely autonomous party."
Former First Minister Henry McLeish also reiterated his support for the idea: "What you have got is this classic disconnect between the Westminster party and the Scottish party and that's why, in my view, after this election you will see a far bigger move towards Scottish autonomy in terms of the Labour Party."
However, Murray said: "I will sit in the House of Commons with 231 of my UK colleagues and we will fight together for social justice and we will fight together for equality and we will fight together to eradicate poverty right across the United Kingdom.
"We share values that run through the Scottish Labour party as well as the UK Labour party like a stick of rock and we have to continue to make that case."
A senior Labour source said there would be "discussions" on moving towards a federal structure, but he said many party members would balk at the idea of an independent party.
The insider said devolving control of MPs' selections was "essential", adding that the Scottish party's executive had "no say" in determining the candidate for Dundee West after the last-minute withdrawal of the ex-MP Jim McGovern.
It is also understood figures close to Murphy are sympathetic to far-reaching reforms of candidate selection for Holyrood selections.
The party has already chosen its candidates for first-past-the-post constituencies, but these contests may be re-run.
On the regional Lists, Murphy is almost certain to scrap a system of "protected places" that can reserve the top spots for sitting MSPs.
It will be replaced by a system that allows any member of the party to come first on a List.
An SNP spokesperson said: "It is entirely a matter for the Labour Party, but of course the wider interests of accountability in Scotland would be served by Labour being run independently north of the border - and not like the 'branch office' it still is under Jim Murphy."
Scottish Labour declined to comment.
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