The idea, outlined in broad terms by former prime minister Gordon Brown in a recent book, is being considered by Labour leader Ed Miliband's policy team, who are drawing up a detailed platform to fight the Westminster election now less than a year away.
It is understood they are looking at proposals for a radically reformed second chamber made up of represen-tatives from Scotland, Wales, Northern Ireland and the English regions.
The body would be "indirectly elected", possibly by elected politicians from the different nations and regions of the UK.
If agreed, the plan would be included in Labour's manifesto alongside proposals to devolve further powers to Holyrood and hand greater control over housing, transport and economic development to the UK's biggest cities.
A source said: "The idea is part of the policy process. If we do this, an incoming Labour government would be a reforming, democratically renewing Labour government as surely as it was in 1997."
As part of Labour's manifesto process, a report by the party's national policy forum will be published next month and form the basis of further discussions during Labour's national conference in late September. The report and conference debates will form the basis of the manifesto.
Supporters of the senate plan, who include many within Scottish Labour, are hopeful it will be adopted, citing Mr Miliband's previous backing for Lords reform as a cause for optimism.
The move could also build bridges with the Liberal Democrats, who fell out bitterly with their Conservative coalition partners when backbench Tories refused to support Nick Clegg's proposed Lords reforms two years ago.
In his recent book My Scotland, Our Britain, Mr Brown describes the House of Lords as "an anachronism" and add that "everyone agrees it needs further reform".
He wrote: "One reform UK parties should consider is making the House of Lords a senate of the regions and nations, elected by the people, responsible for bringing regions and nations together and finding a way of ensuring that where one measure offends one part of the country that is taken into account when making final decisions."
The proposal is seen as an attempt to rebalance the UK constitution.
The proposed senate would give the devolved nations and the English regions a stronger voice and act as a forum to settle disputes.
Under the US system, states enjoy equal representation in the Senate, irrespective of their size or population, in a bid to ensure bigger states do not dominate decision-making.
The principle of hereditary peers sitting in the House of Lords was ended in 1999 but since then reform of the second chamber has stalled.
Before the 2010 election, which Labour lost, Mr Brown pledged to introduce a fully elected House of Lords by 2025 at the latest.
LibDem grandee Lord Steel has also brought forward proposals to replace the Lords with a senate.
Under his plan, 450 senators would be elected by MPs, MEPs, MSPs and members of the devolved assemblies in Wales and Northern Ireland. As with the present Upper House, the senate could delay legislation by asking the Commons to reconsider it, but it would have no power of veto or control over finance.
Lord Steel said last year: "The notion of Lords as part of our legislature is simply ridiculous in the 21st century."
The SNP have argued the cost and undemocratic nature of the House of Lords is a reason for Scotland to leave the UK.