Talks with Spain’s Santander broke down because the two sides could not agree a price, the BBC reports.
As part of its bailout in 2008, RBS was given until 2017 to sell the branches.
It attempted to use them to form a new bank under the Williams and Glyn brand but last month, in the face of rising costs, it abandoned that effort.
Since then, RBS has been looking for buyers for the 315 branches and their associated personal and business accounts, and Santander was seen as the front runner.
But the prospect of a further cut in UK interest rates has undermined that deal, as lower rates cut into the profits of High Street banks – making the RBS branches less attractive.
The sale also comes at a time when banks are reducing the size of their branch networks as more customers are banking online.
Last month RBS reported a $2bn loss for the first six months of the year, which it blamed on past issues, including the mis-selling of payment protection insurance.
It also said that it spent £345m attempting to form the Williams and Glyn unit.