Bank of Scotland and Royal Bank of Scotland would be seen as natural buyers. Both banks have been expanding in Ireland and Britain and are interested in putting down deeper roots in both locations.
They would be "natural buyers" of NAB's European operations, said Stuart Draper, head of research at stockbrokers, Dolmen Butler Briscoe.
However, Mr Stewart who was recently appointed to the top job in NAB, said there were no plans, to sell its British and Irish banks, including National Irish Bank.
He was speaking after underlying earnings at its British and Irish operations slumped 37% due to higher pension fund expenses and currency movements. It could take up to three years to see an improvement in the British and Irish operations.
Given the under-performance of its European operations Mr Draper said there would be a "rationale" for the bank to move now to sell its non-core assets in Europe.
For several years it has been speculated that NIB was too small to make any impact in the Irish market, which is dominated by the core banks.
Mr Draper said yesterday's results should focus minds at NAB particularly in the light of recent events.
NAB reported "disappointing" interim earnings which reflected the impact of a costly rogue foreign exchange trading scandal.
It warned it could take two years to turn the company around.
Still reeling from the trading scandal which he admitted had been "distracting", Mr Stewart said the full extent of the damage was yet to be felt and he forecast earnings in the second half would be "flat at best" in the current year.
Australia's biggest bank boosted headline net profits 16% to €1.2bn (A$2.2bn) for the six months to March. Its own key measure of performance however net cash profit fell 8.7% over the period.
The bank was hit by a €210m (A$360m) foreign currency trading scandal three months ago and the poor performance in the bank's European operations has added to its difficulties. In the light of recent events and its failure to expand its Irish operations, Mr Draper said the future ownership of National Irish Bank was in doubt.
The Irish operation is also waiting for the publication of a major investigation into its operation of bogus non-resident accounts.
Meanwhile, the unauthorised trading of the bank's funds resulted in the sacking or resignation of NAB's chairman, chief executive, chief financial officer and the four rogue traders.
The bank was severely reprimanded by the industry regulator in Australia for lax risk management and ordered to adhere to stricter compliance procedures in the future.