Reports are suggesting that the sale could generate £600m ($1bn).
The bank, founded in the 18th century, is likely to see interest from bidders across the world. However, it is unclear whether the new Coutts International will be kept as one entity or split up. If it is split, one operation would be based in the UK, the other in Zurich, Switzerland.
The Zurich operation would manage around £20bn of assets, primarily in Asian and Middle-Eastern countries such as Hong Kong, Singapore and Dubai.
A memo issued to staff by RBS ahead of the public announcement said:
“We will… work with local management teams to explore options including merging the remainder of the current Coutts International business, considering joint ventures or a sale, thereby reducing RBS’s footprint internationally.
“There are no immediate changes for individuals in these businesses and it is important that we continue to work together to deliver for our customers.”
It will be a further watering down of the bank which saw its, African, Caribbean and Latin American private banking operations snapped up by the Royal Bank of Canada in 2012.
In its present form, Coutts International has a presence in seven countries employing around 1,200 members of staff.