The sale of Ulster Bank, the third-biggest bank in the Republic and the second-biggest in the North, would be the most significant in the Irish financial market in recent years.
Analysts predict the price tag would be at least £2 billion (€2.54 billion) and possibly as much as £2.5 billion.
More significantly, however, given the scale of Ulster Bank, a change of ownership could alter the competitive dynamics of the Irish market.
Irish Life & Permanent is seen as the leading domestic bidder for Ulster Bank if it does come on the market. It has made quite clear its interest in expanding by acquiring a major retail player.
IL&P's chief executive, Mr David Went, was previously managing director of Ulster Bank and would see its network as offering him a chance to turn his organisation into a major competitor to AIB and Bank of Ireland in the financial services market.
Bank of Ireland has been mentioned as another likely bidder, but as a purchase would give it a share of around 50 per cent of the domestic market, it could face competition law constraints.
However, it cannot be ruled out as a bidder and would be particularly interested in the Northern Ireland operations of Ulster.
Likewise, National Australia Bank, which owns Northern Bank in the North and the smaller National Irish Bank in the Republic, would face competition problems in purchasing the Northern Ireland operations of Ulster, as the two combined would dominate that market.
NAB is not thought to have seriously examined the prospect of bidding for Ulster. However, the departure of its managing director, Mr Frank Cicutto, and its chairman, Mr Mark Raynor, from Australia for London led to intense speculation in Australia yesterday that they were moving to size up some of the assets NatWest put up for sale.
Overseas institutions - such as KBC, the Belgian owner of Irish Intercontinental Bank - could also enter the race for Ulster.
Ulster Bank made pre-tax profits last year of £155 million sterling and profits are likely to top £170 million in the current year. It has 113 branches in the Republic - from where it derives 60 per cent of its profits - and 91 in the North.
For its management - which thought it had buried rumours earlier this year that it might be sold to Irish Life & Permanent - the uncertainty over its future promises a difficult period, as for the moment they can merely wait and see how the chips fall.
