Permanent TSB could double in size if it secures the parts of Ulster Bank it is currently involved in talks to buy.
It is understood that the majority state owned bank could acquire the bulk of Ulster Bank's entire €14bn mortgage book as part of a potential deal being discussed.
Permanent TSB may also buy €700m worth of Ulster Bank's SME loans, as well as some of its branches and take on a volume of deposits if the deal is concluded, sources have confirmed.
If PTSB were to buy Ulster Bank branches, it is expected that many of its 76 outlets would be amalgamated with Ulster Bank's 88.
However, how Permanent TSB, which is 75% owned by the state, would fund the transaction is very unclear.
Politically it could prove tricky for the Government to be seen to put more money into an Irish bank.
The Minister for Finance refused to speculate about how the money would be raised, arguing that the transaction would first have to be worked out.
However, he said he would consider any proposed deal if one was brought to him.
A purchase of this magnitude would elevate PTSB into a so-called "third banking force" that could rival the dominance of AIB and Bank of Ireland.
Earlier Permanent TSB confirmed that it was in early discussions with Ulster Bank about acquiring some of its retail and SME business.
This morning NatWest said that it would begin an "orderly and considered" withdrawal from the Republic of Ireland over the coming years following a review of its business.
Ulster Bank has 1.1 million customers here, along with 2,800 staff.
In a statement Permanent TSB said it had "ambitious plans to grow" its retail and SME operations and has entered talks with NatWest about those areas of its Irish business.
However it said there was no certainty that an acquisition would occur, or the terms of any deal.It also noted that any deal it agrees to would require approval by the banks and regulators.
"Permanent TSB is committed to growth and to supporting customers and communities," said its CEO Eamonn Crowley.
"On that basis we are in discussions with NatWest in relation to acquiring certain elements of the Ulster Bank Retail and SME Business to provide continuity of service for customers and to strengthen our ability to provide choice and competition in the market generally."
Separately, AIB this morning announced it had signed a memorandum of understanding with NatWest about the potential acquisition of €4 billion worth of its commercial and corporate loan book.