A Miami-based trial judge, currently presiding over the case of ex-UBS banker Bradley Birkenfeld, has been asked by the prosecutors to allow tax authorities to force the bank to reveal the names.
Mr Birkenfeld has already pleaded guilty to charges that he assisted the clients in hiding around $20 billion of assets, in order for them to cut their income tax payments.
UBS shares dropped 6.9 per cent on the Zurich exchange following the news, Bloomberg reports.
The prosecutors' move represents further bad news for the bank, which has already announced losses stemming from the credit crunch of around $37 billion.
Commenting on the Birkenfeld case in a note to clients, Dresdner Kleinwort analyst Stefan-Michael Stalmann said: "[It] has the potential to develop into a serious strategic headache for UBS in its most profitable business.
"There is a clear risk that the damage will reach beyond whatever the direct cost of a settlement or fine will be.''