Sky News reports that Santander "has tabled a formal offer to acquire the network... in the last few days", but that the deal was still uncertain.
In May, RBS announced plans to rebrand 300 of its branches to Williams & Glyn.
RBS hopes to separate Williams & Glyn as a standalone challenger bank by 2017, but admitted in its full year results that it continues to face "significant challenges and risks in separating the Williams & Glyn business".
RBS says that "due to the complexities of Williams & Glyn's customer and product mix, the programme to create a cloned banking platform continues to be very challenging and the timetable to achieve separation is uncertain".
In its annual report, RBS said: "In particular, Williams Glyn is a complex business and unforeseen difficulties in integrating the business with that of any buyer could deter potential buyers from bidding for the business or completing the sale. In addition, the number of potential bidders with synergy potential or strategic interests may be limited and such investors may value the business below what the Group considers to be the fair value of the Williams & Glyn business."
In Q1, Williams & Glyn new lending increased by 50% to £1.4 billion compared with Q1 2015. Notably, new mortgages were up 107% to £581 million, which RBS said were driven by a "more buoyant market, greater productivity and more competitive pricing".
Williams & Glyn separation costs have totalled £630 million to date.
When separation is complete, RBS says Williams & Glyn will be of the UK's largest banks with around a 5% business market share. It expects to have total assets of £20bn and customer deposits of £23.6bn.
