Blackstone, the US financial services giant, and BDO Stoy Hayward, the UK accountancy, are believed to be in the running to value Bradford & Bingley, the nationalised bank.
The Treasury has accepted pitches for the job, which will determine how much shareholders should be compensated and will interview the shortlist next month. An appointment is expected in the summer.
The job is a lucrative one: BDO has been paid about £4.5m to value Northern Rock, and B&B is thought to be a much more complicated task.
It is understood that BDO was not ruled out of the running, despite some speculation that it could have a conflict of interest by working on another nationalised bank valuation. KPMG, one of the big four accountants, was ruled out, as it was B&B's auditor.
Bankers said that they were frustrated by how long the appointment process has taken since B&B was nationalised last September.
The job's scale has also put off some prospective bidders. "We're quite wary of this kind of work," said a financial services source who decided against a pitch. "You do get good short-term fees, but it really is quite a lot of work."
Almost one million investors will have to be contacted for the sensitive information needed to determine the compensation for the nationalisation, which wiped out shareholders' stakes.
The selection will be made by a four-strong panel chaired by Michael Izza, the chief executive of the Institute of Chartered Accountants in England and Wales. Anthony Fry, senior managing director at boutique investment bank Evercore Partnership, is also on the panel.
When B&B was nationalised, its profitable savings business was sold to Abbey, owned by the Spanish group Santander. The Government has ruled out turning B&B into a "bad bank" into which the nationalised banks would have poured all their worst assets.
Many restructuring advisers are still lobbying the Government to create a bad bank. They argue that by getting rid of their worst assets, most of the nationalised banks would be far stronger and could easily buy back the Government's investment. "The Treasury must want to get banking assets off the Government's balance sheet," said a banking source. However, a Treasury insider ruled out the move.