Irish Life & Permanent and AIB are expected to submit final bids for TSB Bank today.
The bids will be sent to TSB's advisers, Pricewaterhouse Coopers, and will then be evaluated TSB's trustees.
Industry sources suggest the bids will value the bank at about £330 million (€419.01 million).
The final bids follow presentations by both banks to the TSB trustees in July.
The trustees will then decide whether to accept one of the bids or to seek to convince the Minister for Finance, Mr McCreevy, of a viable alternative for the bank.
A trade sale is expected to be the final outcome and a decision should be reached before the end of the year.
Opinion is divided over which bank would be the preferred option for the TSB. Many analysts believe Irish Life & Permanent will emerge as the new owner with AIB acting as a spoiler to force it to pay a high price for the bank.
But within TSB, there is a view that AIB may be the more viable option.
The TSB offers Irish Life & Permanent access to the bank clearing system and is an important strategic objective for the banking and life assurance group. Such an acquisition may, in turn, flush out a bid for Irish Life & Permanent in the near term. There are concerns that this will create further uncertainty for TSB employees.
A takeover by AIB would bring the bank within the State's biggest financial institution. Under the terms of the sale, both banks must lodge a bid for 100 per cent of the TSB with the staff's 14.9 per cent stake to be addressed at a later date.
Any deal must be sanctioned by the Minister for Finance and the proceeds of the sale will go to the Exchequer.