Greek depositors withdrew €700 million (£557 million) from banks on Monday, according to the country's president.
Greek banks have seen a steady decline in deposits since the country's debt crisis began in 2009, as depositors have withdrawn cash and transferred funds to overseas banks.
In the past two years, deposit outflows have averaged between €2 billion and €3 billion per month, though in January they topped the €5 billion mark.
Greece will hold new elections next month after party leaders failed to find an agreement on a coalition Government.
As well as traders preparing for the return of the Greek drachma some UK companies are considering a eurozone exit strategy.
A business leader said if there was a sudden deterioration in the eurozone it would be like an 'earthquake' for British firmS.