The British government-backed Royal Bank of Scotland (RBS) plans to sell the international arm of its private bank, Coutts, in a deal that could be valued at about $1bn.
The sale could see RBS rake in between $720m (£429m, €538m) and $1.1bn, based on a multiple of 2% to 3% of assets under management, Reuters reported.
Asian and North American investors have bid for Coutts International, the report said.
RBS has refused to comment on the news.
RBS' stock was trading 1.59% lower at 12:40 BST in London.
The move will split Coutts – the banker to the Queen of England – into two businesses: one based in Britain; another in Zurich, Switzerland, from where it runs operations in Hong Kong, Singapore, Monaco, Dubai and Abu Dhabi managing assets worth about $36bn.
RBS said last week that it was "reviewing" its private banking business. The lender has noted that since Coutts' international clients are richer than those in the UK, splitting the businesses will make sense as services required by both client groups are different.
RBS has been under pressure from lawmakers to focus on lending to UK households and businesses to help buoy the nation's economic recovery.
In 2013, Coutts International's operating profit was 103m Swiss francs (€84.8m, £67.7) excluding provisions.
RBS is 81% owned by the state of the United Kingdom, following a £45bn bailout after the 2008 financial crisis.