Mills has created a website, Couttsaigactiongroup.org, for the campaign in an attempt to encourage other wealthy clients of Coutts to pressure the private bank into paying compensation, according to a report in The Times.
According to Mills, Coutts recommended that he buy AIG Life Premier Bonds as a safer alternative to bank deposits.
Mills had £160m to bank after last year's sale of Loyalty Management Group, the Nectar business, and he is thought to have a substantial sum tied up in AIG bonds.
AIG bondholders' money was frozen in September after investors began rushing to redeem their money following revelations of AIG's huge losses in the US, which led to a bail out by the US Government.
Investors now stand to lose about 13.5p in the pound if they attempt to take their money out, according to the report.
Coutts told The Times that the bonds were sold with the appropriate advice.
The bank said: "At the time of sale it was made clear that the investment was low risk but not risk-free, and that the value of the investment could go up as well as down."
Coutts is reportedly lobbying AIG on behalf of its clients to negotiate the best deal possible.
Mills's campaign raises the possibility of some of Britain's wealthiest people applying for compensation from a bank owned by RBS, which is now 58% owned by the government, and therefore funded by taxpayers.
RBS shares dropped 8% yesterday to 46.5p following speculation that the bank might need more money from the Government, on top of the £20bn it has already received.
This article was first published on brandrepublic.com