"This is normal surveillance linked to following the rules aimed at blocking money laundering," FINMA chairwoman Anne Héritier Lachat told AFP on Tuesday on the sidelines of the regulator's annual conference in Bern to assess its activities.
FINMA has not yet seen the need to take special measures to meet a possible influx of cash from Cyprus, where all the banks remained closed for an 11th day Tuesday to avoid a run following a crippling bail-out deal with the European Union.
"So far, this will be handled within the framework of normal surveillance, and the institutions know perfectly how to apply these diligence rules," Héritier Lachat said.
Cyprus secured a deal with the EU on Monday for a 10-billion-euro ($13 billion) bailout that helped it avert bankruptcy but which will see large deposit-holders at its two biggest banks losing much of their savings.
The banks are being kept closed amid fears of bank runs and that foreigners, and especially Russians, will move their funds out of the country.
Figures vary but the Moody's rating firm estimates that Russian companies and banks keep up to $31 billion on the Mediterranean island, which accounts for between a third and half of all Cypriot deposits.
Switzerland with its banking secrecy rules was long considered a prime destination for undeclared funds, but the country has in recent years been cracking down in a bid to clear its reputation as a tax haven, and has made clear it has no interest in taking in illegal cash from Cyprus.