According to Sky News, Investec is understood to have hired advisers to help it consider a possible acquisition of the firm, which could be sold by Royal Bank of Scotland (RBS) for between £500m to £650m.
Investec is the latest in a series of firms interested in acquiring the international arm of Coutts, which has been put up for sale by RBS. A disposal of the business is expected to take place later this year
There are believed to be 10 potential bidders for the firm including Societe Generale, BNP Paribas and Julius Baer.
Meanwhile, Italian bank Intesa Sanpaolo is reportedly interested in buying the entirety of the wealth manager, including its UK business.
However, RBS has announced no plans to sell the UK arm and is said to be keen on retaining this part of the Coutts brand.
Coutts International operates across seven countries with 1,200 employees and $35bn in AUM, with a third of this coming from Asia.