A fund manager said that the shares were being offered at an indicative price of HK$26.75 to HK$27 a share, raising as much as HK$2.16 billion ($277 million) for the firm.
Temasek had a 5.72 percent stake in COSCO, according to Reuters Data, and this sale represents more than half of its holdings.
Goldman Sachs handled the sale, a banking source said.
On Wednesday Temasek sold $255 million worth of shares in China Construction Bank , which followed the sale of a stake worth $571.5 million in Bank of China -- potentially raising over $1.1 billion dollar from stake sales.
Temasek spokeswoman Myrna Thomas said the sale "is part of our ongoing rebalancing of the portfolio against new opportunities".
Earlier this month Temasek said it would pay $315 million for a 8.27 percent stake in China Eastern Airlines