State-backed RBS has to offload the branches by the end of next year as a condition of the £45 billion bailout it received at the height of the financial crisis.
The Edinburgh-based group had been planning to float off the business under the old Williams & Glyn brand, but has now focused its efforts on sealing a trade sale.
Santander abandoned a £1.65bn deal for the branches in 2012, before returning to the negotiating table earlier this year. However, it has been reported that talks with Santander have broken down because of a disagreement over the price of the Williams & Glyn branches.
RBS last month reported a loss of £2bn for the first half of the year, compared with a £179m loss a year earlier, after being hit by extra restructuring costs and an increased bill for mis-sold payment protection insurance.