Foreign investors have offered between 15 and 16 billion euros ($19.4-20.7 billion) of Greek government bonds in a debt buy-back programme, according to an initial estimate given by newspapers on Saturday.
The plan is central to efforts by Greece's euro zone and International Monetary Fund lenders to cut its borrowing to manageable levels and unlock aid.
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The preliminary estimate cited by financial dailies Naftemporiki and Imerisia would suggest the buyback plan is on track to succeed.
Under the plan, Athens aims to spend 10 billion euros of borrowed money to buy back bonds with a nominal value of about 30 billion euros ($38.8 billion). Since the bonds would be bought far below their nominal value, the country's net debt burden would fall by about 20 billion euros.
The papers said the final figure for offers from foreign investors may increase once Greece's debt agency completes an evaluation of them.
A deadline to submit the offers expired on Friday. The newspapers did not say how they had come by the initial numbers.
Greek lenders, which hold about 17 billion euros worth bonds, already announced on Friday that they would take part in the buyback.
(Reporting by Harry Papachristou)