The sale of the private bank of Royal Bank of Scotland has attracted about 10 suitors in the initial round, and could fetch about $1bn (£656m), Reuters previously reported.
No firm date had been set for the final bids, the people added, but all the shortlisted parties had commenced due diligence.
DBS, which is mainly interested in the Asian unit of Coutts, had teamed up with French bank Societe Generale which could buy the European business, they said.
Julius Baer and South Africa’s Investec had also made it to the next round, they said, while a one person said Credit Suisse was also among the bidders shortlisted.
Spokespeople for DBS, Sarasin Credit Suisse, Investec, Societe Generale and Julius Baer declined to comment.
Coutts was founded in the 18th century and is best known as banker to Queen Elizabeth II.
Under the proposed restructure, Coutts could be split into two businesses – one based in London and one in Zurich from where it runs operations in Hong Kong, Singapore, Abu Dhabi and Dubai.
Around one-third of the nearly $36bn in assets managed by the bank came from Asia, Reuters previously reported.
RBS’s preference is to sell the business as one entity as opposed to breaking it into European and Asia bits.
The sale comes as RBS, which is majority owned by the UK government, is retreating from sub-scale businesses and markets.