RBS has until Thursday to reach a deal while Lloyds has until Friday
Taxpayers may become liable for £500bn worth of bad loans and investments made by Royal Bank of Scotland and Lloyds Banking Group, the BBC has learned.
It would be part of the government's Asset Protection Scheme, under which taxpayers insure banks against future losses from such assets.
RBS has a Thursday deadline to agree terms, while Lloyds has until Friday.
The idea is to draw a line under bad assets to free up cash that the banks can lend to companies and individuals.
BBC business editor Robert Peston says that if the deal is completed, it will take the total support by British taxpayers to the banks to £1.3tn.
ASSET PROTECTION SCHEME
Taxpayers underwrite banks' bad debts
Essentially an insurance scheme
Banks pay a fee to take part
Banks are liable for the first 10% of any losses, similar to paying the excess on an insurance claim
First announced in January
That figure, made up of loans, guarantees, insurance and investments, is equivalent to the entire annual output of the UK economy.
RBS and Lloyds are understood to be hoping to insure £250bn of assets each.
One of the sticking points in the negotiations is the amount of losses the banks would have to take themselves before the taxpayer started paying.
The original plan under the Asset Protection Scheme was that the banks would pick up the first 10% of losses, but forcing RBS and Lloyds to take on £25bn of losses each would risk weakening rather than strengthening them.
There is also the question of what fees the banks would have to pay for the insurance.
The fees are expected to be paid in preference shares, which would not carry voting rights, so that the government's stake in the banks would not increase above the current 70% of RBS and 43% of Lloyds.
But it could mean that the government's control over the banks' profits and assets could approach 100%, which according to Robert Peston would amount to economic nationalisation - if not formal nationalisation.