UK Labour shadow chancellor John McDonnell has called for a "radical federal" UK.
The move would signal a major change in the UK Labour Party's position when it comes to the constitutional settlement in Britain.
The Sunday Herald has also learned that other senior figures in Jeremy Corbyn's shadow cabinet are also looking at formally adopting federalism as party policy.
Last night, McDonnell, Corbyn's closest ally, gave the clearest indication yet that Labour will legislate for the UK to become a federal state if it wins the next General Election.
Speaking to the Sunday Herald, McDonnell said: “I believe there is immense potential in developing a radical federal structure [for the UK].”
Meanwhile, former London mayor Ken Livingstone told the Sunday Herald he was "certain" Labour under Corbyn would embrace federalism. Livingstone also stated his own support a federal UK - which would be the most radical shake-up of the UK's constitution since devolution.
The left winger, who was also elected twice as London mayor, said that he was convinced Corbyn and McDonnell would promote federalism as an alternative to both Scottish independence and the status quo of the Union.
Livingstone said: "I'm certain that they will. John McDonnell like me came into politics from local government to make sure that wealth and power are fairly distributed across all regions."
Federalism - a policy so far only embraced by the Lib Dems at UK level - would see national parliaments in Scotland, Wales and Northern Ireland have power over all legislative matters except foreign affairs and defence.
Scottish Labour leader Kezia Dugdale has also backed federalism. In a major speech in London last month, she said the UK needed “a new political settlement” to stop an erratic and uneven distribution of power between its regions and nations.
Dugdale said the UK should be transformed into a federal state with Scotland taking control over fisheries, farming and social rights now covered by EU laws. Former Labour Prime Minister Gordon Brown backed a similar package.
Speaking this week, Dugdale said: "I have proposed a federal solution, where every nation and the regions of England could take more responsibility for what happens in their communities – while firmly safeguarding the redistribution of wealth across the UK."
UK Labour's national elections coordinator Jon Trickett is understood to be examining a radical policy package for the party at Westminster to deliver a federal British state if it wins the 2020 General Election.
Trickett, who is Corbyn's lead on constitutional issues, is a strong supporter of devolution to the UK regions as a former leader of Leeds City Council and an MP for Hemsworth in West Yorkshire.
He has also held talks with figures in Scottish Labour on how the party could use a federal structure for the UK to promote a left-wing agenda by the redistribution of wealth through the parliaments in Edinburgh, Cardiff and Belfast, as well as the English regions.
Livingstone, commenting on the proposals, said such an agenda for the party north and south of the Border would "help" it to develop an alternative to Scottish independence and the status quo of the union.
Speaking to the Sunday Herald, Livingstone said: "There are about a dozen places that would benefit from federalism, including the Welsh and Scottish Parliaments. It would help, but the fact is people voted against independence.
I support Jeremy [Corbyn] because he's got ideas about moving away from a society where the 10 per cent control most of the wealth. The SNP poses itself as of the left and talks left, but it definitely doesn't act in the same way."
Livingstone, who served as a Labour MP in London for 14 years, also claimed federalism would make it less likely that any region of the UK can be dominated by "little elites".
He said: "I've always been in favour of devolving power to whatever region we're talking about. If you look at America or Germany, states and regions have real local recognition unlike in the UK where all the power is sucked up by Whitehall.
"I've advanced the devolution approach all my political career. If you'd had north east and north west regional parliaments or assemblies they would have got massive investment. So federalism absolutely. We need it as people in regions in all parts of the UK are being excluded by little elites."
However, Chris Stephens, the SNP MP for Glasgow South West, said independence would make it easier to deliver social justice than federalism.
Stephens, the SNP's trade union and workers' rights spokesman at Westminster, said: "The clear difficulty with federalism is that there appears to be a lack of enthusiasm for it elsewhere in the UK.
"In terms of autonomy on issues such as employment law and workers' rights, independence remains the best option for those seeking a different approach to the Tories and their current hatred for trade unions and progressive politics."
Andrew Whitaker, The Sunday Herald, 8th January 2016