Shell has been looking for buyers for its stake in the project, which pumps 100,000 barrels a day from fields in the North West Shelf region.
According to the South China Morning Post, CNOOC has hired the Macquarie Group to arrange a potential bid.
Other partners in Cossack-Pioneer are Woodside, BHP Billiton, BP, Chevron, and a joint venture between Mitsubishi Corp and Mitsui & Co.
The Asia-Pacific region is recognised as one of the areas in which CNOOC wants to build its core business.
In July, CNOOC strengthened its footprint in Australia by securing a permit to explore in the Bonaparte Basin.
