Bank of England in car maker loan talks
The Government wants cash from the scheme to fund the finance arms of car companies to stimulate new vehicle sales, but Mr King has so far refused.
Suggestions for a compromise scheme, involving the nomination of a bank to handle the flow of money, have been under discussion over the past week.
Car makers have been increasing the pressure on the Government to give them access to the special liquidity scheme, as sales show no signs of improving.
Meanwhile, Business Secretary Lord Mandelson has also stepped up plans to provide financial incentives for car owners to scrap old cars in return for buying new and more economical models.
Lord Mandelson is in discussions with the European Union over how such a scheme would be funded and administered.