Bank of Ireland and AIB are set to pass the latest series of stress tests carried out by the European Central Bank, but Permanent TSB has reportedly failed.
Stress tests examine whether banks have enough funds to withstand a severe economic downturn.
The chief executives of the banks have already been told whether or not their institutions have passed the stress tests, but the results will not be made public until around 11am on Sunday.
The ECB has asked banks not to make any disclosures until this point.
However, sources have said Permanent TSB has failed one of three stress tests.
Mortgage arrears and a large number of tracker mortgages have weakened Permanent TSB's finances.
It is expected Permanent TSB will have to raise hundreds of millions of euro to make up the shortfall.
To do so, it will sell shares on the stock market, which would see the State's 99% stake in the bank reduced.