The sale will generate approximately pounds 40m in cash for MAM as the deposits of Mercury Bank had been consolidated on MAM's balance sheet.
Stephen Zimmerman, deputy chairman of MAM, said the group was considering redistributing the proceeds of the sale to shareholders.
"We will be looking at ways, if we don't have use for the cash, [to return it to shareholders]," Mr Zimmerman said.
He said MAM would not know if it needed the cash until the time of its results in March.
And before returning any cash to shareholders the company would need clarification of the tax implications of share buy-backs and large dividends following the recent action taken by Kenneth Clarke, the Chancellor.
The decision to sell the private bank is part of MAM's strategy to concentrate on its core investment management business and its UK and Jersey-based international private client operations.
In addition, MAM will manage a "significant" pool of assets for Republic National, which specialises in private banking. It is 100 per cent- owned by Safra Republic Holdings, which in turn is part of the Republic New York Corporation Banking Group.
MAM will keep its representative office in Zurich, which markets mutual funds and investment services for institutional clients.