Michael Ambühl, Switzerland's State Secretary, and Ilias Plaskovitis, the General Secretary from the Greek Finance Ministry, "discussed the possibility of a tax agreement like the ones Switzerland signed a few weeks ago with Germany and the United Kingdom.
"The aim is to regularise the assets held by Greek taxpayers in Swiss bank accounts in the past as well as to introduce a tax at source on future investment income," the Swiss authorities said.
"In the coming weeks, both countries' governments should decide on the actual initiation of negotiations," they added.
Swiss media estimate that some 350 billion francs ($405 billion) in Greek assets are hidden in Switzerland.
However, the financial industry believes that estimate is too high.
"The 350 billion francs raised by certain media have nothing to do with what is in Switzerland," said Bernard Droux, who heads the Geneva financial industry association.
According to one rare study by Bank Helvea on hidden assets from 2009, undeclared Greek funds totalled 24 billion francs.
The Swiss National Bank has an even smaller figure -- according to last year's data, some 4.1 billion francs in Greek assets are held in the Alpine state which has come under international pressure over its traditional bank secrecy laws.
As a result, it has signed many tax deals with critical countries to ensure more information about foreign holdings in Switzerland is available, allowing tax to be levied on them.