RBS overnight received preliminary offers from at least five bidders for the network of 318 branches in England and Scotland that it is being forced to sell.
BBC's business editor reported that the five were Spanish banks Santander and BBVA, Virgin Money, National Australia Bank and private equity firm JC Flowers.
RBS may refine this shortlist to two,
BBC reported, and expects to select the preferred bidder by July or August.
In an interview with the
Financial Times, Wilbur Ross, the US investor who is investing directly in Virgin Money and also alongside Virgin Money's bid for RBS, made clear that the partners were bidders for the RBS assets on realistic terms.
"If Santander or some other non-UK entity makes a 'wow' bid we'll lose," Mr Ross told the newspaper. "We're only interested if we can get it at a reasonable price."
The FT reported that Santander is understood to have tabled an initial bid of up to £2.5 billion last week. The FT also reported that Virgin was expected to offer a lower price, of about £1 billion to £1.5 billion.