The deal could be valued as much as $6bn, The Wall Street Journal reported.
Cigna non-health benefits unit offers insurance plans including accident and disability-income as well as life insurance policies.
Part of disability and other operations division, Cigna’s group benefits business reported $1.31bn of adjusted revenue in the three months to 30 June. It serves 15.4 million customers.
Reuters first reported in August that the business has been put on sale.
If the proposed deal materialises, it will strengthen New York Life business outside the core business of life insurance and annuities.
Sources familiar with the development told the publication that New York Life and Cigna are expected to announce the deal as early as this month.
However, they cautioned that there is no certainty about the deal, as other potential suitors such as Sun Life Financial and MetLife are also vying for the business.
Cigna has been looking to cut down its debt obligations after it purchased pharmacy-benefits manager Express Scripts for a $54bn last year.
Following the completion of the transactions, Cigna debt pile rose to over $40bn.