The deadline for bids to be in is 23 August and the Irish bank is expected to fetch around Irpounds 300m (pounds 288m). ABN-Amro, the investment bank, is advising the Irish government on the sale.
Other UK-based bidders are likely to include National Westminster Bank, which already has a presence in Ireland through its offshoot Ulster Bank. Bank of Ireland, which recently failed to merge with Alliance & Leicester, is also believed to be interested.
Irish Life & Permanent, Ireland's third largest bank, has ruled out bidding for ICC because it believes that the price the Irish government is seeking is too high.
Bank of Scotland refused to comment on its expected bid, but it has been looking to expand its operations both within the UK and overseas.
The attraction of ICC Bank to Bank of Scotland, as it is for NatWest, is that it would provide a way into Europe's fastest growing economy.
The Irish government is forecasting GDP growth of 7.5 per cent this year with inflation at 1.8 per cent. Retail sales have expanded 10 per cent so far this year and car sales are up by 21 per cent.
The Irish banks have been enjoying bumper profits as a result of the boom. ICC last month reported a 25 per cent rise in profits to Irpounds 11.3m while lending was up 28 per cent to Irpounds 1.6bn. The bank's lending is mainly to small and medium-sized businesses.
As well as ICC, the Irish government is planning to merge two other banks, ACC and TSB prior to selling them off next year, although the government's preference is for a flotation, rather than a trade sale as with ICC.