The Treasury is reportedly considering trying to persuade the Irish government to take control of Ulster Bank.
Ulster is part of the RBS Group, which is largely owned by the UK taxpayer.
RBS's future is being considered by the Parliamentary Commission on Banking Standards.
The BBC's business editor Robert Peston said that a draft report from the commission called for the split of RBS into a good bank and a bad bank.
However, he added that "another, more radical option is also being assessed by the Treasury".
That would involve somehow removing Ulster Bank from RBS Group - Ulster has been the worst performing part of the group, dragging down its overall performance.
Mr Peston said that one idea raised is to "transfer Ulster Bank into the arms and ownership of the Irish government", by swapping all or part of the bank for the British loans and investments currently owned by Ireland's "bad bank", the National Asset Management Agency (Nama).
Nama manages problem debts on behalf of the Irish government.
Northern Ireland finance minister Sammy Wilson said that Ulster Bank needed to be "divided up into a good bank and a bad bank".
However, he said there were "other options" apart from an Irish government takeover and that he wished to discuss these with the Treasury and the Northern Ireland enterprise minister Arlene Foster on Tuesday.
"Whether or not letting the Irish government take it over is the correct way of dividing the bank up is another matter," he added.
Mr Wilson said the Irish government had "its own problems with its own banking system".
Ulster Bank has £37bn of assets (loans and investments) on a risk-adjusted basis.
Nama is not making any comment on the speculation, but senior financial sources in Dublin are saying that such a move is highly unlikely.
The sources point to the fact that many of Nama's best income-producing assets are in the UK - almost a fifth of its portfolio is in London.
The agency would not want to swap those assets for Irish properties that are likely to be of much worse quality.
The Treasury plan would also face opposition from the Troika of the International Monetary Fund, European Union and European Central Bank that has funded Ireland's bailout.
A Dublin source told the BBC "we would be effectively asking them to double their bet on Ireland".
The Department of Finance in the Irish Republic said no approaches have been made about Ulster Bank.
In a statement, Ulster Bank said: "While we do not comment on speculation, Ulster Bank is a core part of RBS Group and continues to make significant progress.
"As part of our central role in the Northern Ireland economy, we have provided more than £1.5bn in new mortgage lending since the property price peak, resulting in over 15,000 new mortgages, and through the Funding for Lending scheme we have approved lending of more than £70m to over 400 local businesses.
"We have a 177 year history of serving Northern Ireland customers and our commitment to the local market was underlined recently with the appointment of Ellvena Graham as Ulster Bank's Head of Northern Ireland.
"We have the largest branch network in Northern Ireland and remain committed to meeting the needs of our customers."
In February, Ulster Bank reported losses of more than £1bn for 2012, a slight increase on the previous year.
It came as the bank's parent group, Royal Bank of Scotland (RBS), confirmed losses of more than £5bn for 2012.
UK Independence Party assembly member David McNarry has called on the Northern Ireland Executive to seek "immediate guarantees" on the future of Ulster Bank.
"If this is true it will send shockwaves through the whole banking sector in Northern Ireland," he said.