Institute of International Finance director Charles Dallara, who represents the private sector investors and banks that hold Greek debt, said "it's not entirely clear" how close the parties are to a deal.
"I wouldn't say I'm confident, but I'm hopeful we'll reach agreement," Dallara told CNN International's Richard Quest in a phone interview from Athens.
The talks ended Wednesday without an agreement. They will resume Thursday and Dallara said final terms could be reached in the days ahead.
The IIF has been in discussions with the Greek government over an agreement to voluntarily write down the value of Greek government bonds by 50%.
The private sector holds over €200 billion worth of Greece's total debt load -- estimated at €350 billion.
Dallara said the group intends to follow through on the 50% writedown, which was announced following a summit of European Union leaders in December.
That would result in significant losses for the private sector. But it would also help reduce Greece's debt load to 120% of economic output by 2020.
In addition, Dallara said 15% of the remaining amount that Greece owes the private sector would be paid in cash. Another 35% would be restructured, or replaced with loans that have longer maturities and lower interest rates.
The talks broke down last week amid demands for even larger write downs, and Greek Prime Minister Lucas Papademos' call for a private sector participation rate of 100%.
Dallara told CNN he's confident the group can "mobilize a high participation." But that doesn't mean 100%, he added.
The deal is a key condition for Greece to receive additional bailout funds from the European Union and International Monetary Fund. Without additional financial support, Greece may not be able to make a €14 bill! ion paym ent it owes on bonds coming due March 20.
Dallara stressed that both sides are interested in finding "common ground."
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He said the creditors recognize that a portion of Greece's debt needs to be written off in order to avoid a "disorderly" default, which could have severe repercussions for the global economy. But he acknowledged that some investors may be worried that other euro area governments could extract similar concessions.All governments have an interest in resolving Greece's debt problems "in a cooperative manner" so that investors will be confident that issues this extreme can be resolved "in a mutually satisfactory way," said Dallara.
-- CNN's Jim Boulden contributed to this report from London.