The suitors include Credit Suisse, Julius Baer and Malayan Banking and first-round bids are expected to take place before Christmas, sources told Reuters.
Following the sale, RBS, which is owned by the British government, is expected to receive about $1bn and will be able to concentrate on domestic lending.
The private bank manages about $36bn and one third of this amount comes from Asia, reports Reuters.
Companies including Singapore lenders DBS Group and United Overseas Bank, Societe Generale, HSBC, Bank J Safra Sarasin, BNP Paribas and Bank of Montreal in Canada have received the sale documents from RBS.
The sale documents are said to comprise financial as well as other details.
Headquartered in London, Coutts is the wealth division of Royal Bank of Scotland Group, with clients from over 40 offices in financial centers in the UK, Switzerland, the Middle East and Asia.
International banking and financial services company RBS Group serves over 30 million customers in the UK, Europe, the Middle East, the Americas and Asia.
Image: The Royal Bank of Scotland (RBS) Head Office Istanbul. Photo: courtesy of Reise Reise
