In a statement filed with the Singapore Exchange on Saturday, NOL said the talks were "preliminary" and were in relation to "a potential acquisition" of the Singapore firm.
"NOL has a duty to assess all options to maximize shareholder value and improve its competitiveness," the statement said.
It added however that "there is no assurance that any such discussions will result in any definitive agreement or transaction, or that any offer for NOL will be made".
Marseille-based container transportation and shipping company CMA CGM has made a preliminary offer for NOL, which has a market value of Sg$2.7 billion ($1.9 billion), Bloomberg News reported, quoting people with knowledge of the talks.
CMA CGM is carrying out due diligence on NOL, which is 65 percent owned by Singapore state-linked investment firm Temasek Holdings, although the French shipping firm has not been granted exclusivity, Bloomberg added.
Maersk is also talking separately with NOL but the discussions are less advanced, Bloomberg said.
NOL has been racking up losses due to sluggish global trade and lower freight rates.
Last month, the company reported a net loss of $96 million for the third quarter, widening from a loss of $23 million in the same period the year before.
NOL this year sold its logistics business -- APL Logistics Ltd. -- to Japan's Kintetsu World Express Inc. for $1.2 billion.