"Constructive discussions continue on the voluntary debt exchange as other matters move forward," said Frank Vogl, spokesman for the Institute of International Finance which represents the banks.
"We hope that the various elements of the Greek package will come together in the days ahead," he added.
Beyond debt restructuring talks, Greece is also in negotiations with its public creditors -- the European Union and the International Monetary Fund -- to finalise a new series of measures in order to unlock 130 million euros of loans which were promised by the eurozone in October.
On Wednesday afternoon, Greek government spokesman Pantelis Kapsis said that negotiations with banks were at a critical point and that an accord, as well as conditions to unlock new loans, would be finalised in coming days.
Late Tuesday, Finance Minister Evangelos Venizelos said that a deal with private creditors could be submitted to parliament by February 13, and would see banks writing off "over 70 per cent" of Greece's debt.
Until now, private creditors have agreed only to reduce the value of their holdings by a face value of 50 per cent, with further losses expected once details of a bond replacement scheme have been hammered out.
Greece and EU partners have set a February 13 deadline to issue new bonds, as Athens must repay 14.5 billion euros worth of debt on March 20.
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