Sources close to RBS have confirmed it is considering an offer from Santander UK for its Williams and Glyn brand.
RBS is obliged to sell the 300 or so branches, with nearly two million customers, in order to meet state-aid rules as a result of its 2008 bailout.
RBS is also considering a public sale of shares in a new independent business and retail bank.
Hiving off this part of the business has been beset by the difficulty of developing a new IT system.
RBS has already spent over a billion pounds on trying to develop a separate IT platform for the new division.
Lloyds Banking Group experienced similar difficulties and costs in separating out the business now owned by Spanish bank Sabadell and trading under the TSB brand.
The vote to leave the European Union is not expected to affect the decision to offload the business as the deadline for its completion arrives before the UK will have exited the EU even if the mechanism to leave (Article 50) is triggered imminently. The government has said that is unlikely before the end of the year.
The re-emergence of an independent Williams and Glyn on the High Street was supposed to be an important milestone in creating more competition in a banking sector still dominated by five big players (HSBC, RBS, Lloyds, Barclays, Santander).
A sale to Santander would frustrate that objective.
A number of other new small entrants - so called challenger banks such as Aldermore, Shawbrook, Metro and Virgin Money have struggled to gain sufficient scale to mount that challenge. Some have been more severely affected by Brexit as they have sought to cater for underserved, and in some cases riskier, markets such as buy to let and commercial property.
Talks with Santander are still ongoing and could yet fall apart.
RBS is not expected to announce any definitive agreement when it releases its latest results on Friday, which are expected to reveal further losses as restructuring charges continue to offset profits at its core business.