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.
"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, which includes the construction costs of the Hambantota port.
Gwadar Port to begin trade activities today
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.
Ranatunga said the Chinese had initially wanted the port on a 199-year lease.
"First they wanted it for 199 years, then brought it down to 99 years, but I am thinking around 50 years," he said, adding that a final agreement could be signed in January.
Some 480 temporary dock workers at the port in Hambantota, 240 kilometres (150 miles) south of Colombo, have been on strike since December 6 demanding that they be absorbed into the main port-owning company ahead of any sale to the Chinese.
Ranatunga said he had given strikers a Thursday deadline to report back to work or lose their jobs.
Sri Lanka's navy opened fire at the port on Saturday to disperse strikers who had blocked a Japanese vehicle carrier from leaving the port.
The minister said the strikers had also sabotaged facilities at the port, where there were currently no foreign vessels.
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