Arjuna Ranatunga said talks were under way with China Merchants Port Holdings to transfer an 80 percent stake in the Hambantota port on a long lease.
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“We hope to be able to raise about $1.12 billion and a deal could be struck by the first week of January,” Ranatunga told reporters in Colombo.
The new government, which came to power in January last year, has been trying to renegotiate terms of its $8 billion Chinese debt.
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The former administration relied heavily on China to build ports, highways and railways as Western nations shunned it over its dismal human rights record.
The new government secured a $1.5 billion bailout from the International Monetary Fund in June after facing a balance of payments crisis and has also negotiated cheaper funding from international lenders.