According to the Telegraph, lawyers acting for Sir Keith have served the bank with a letter of claim, which is the first step towards launching a legal action over alleged negligence.
The case centers on investments Coutts made in AIG bonds in December 2007, which Sir Keith claims were presented to him as low-risk, easy access assets.
"Coutts said these bonds were an alternative to a traditional bank but the reality was that this investment was far riskier," he said.
Sir Keith also claims to have aired concerns about the investments in March 2008.
The allegations have been denied by Coutts. The bank told the newspaper that AIG has refunded half of all investors' funds and has undertaken to repay the rest.
Coutts is the private banking arm of the Royal Bank of Scotland.