A Cigna spokesman declined to comment on the rumored deal. Anthem did not immediately respond to requests for comment.
Analysts say that because of caps on the profit that insurers can make on their plans, the companies have been looking to cut administrative costs by increasing their scale. The larger companies will also have increased clout in negotiating rates with hospitals and doctors groups.
While the deals make business sense, it is far less clear what impact the mergers will have on customers.
Some analysts say that the growth of insurance premiums could slow because the industry is regulated and the new companies will be more efficient. However, a 2012 study of the 1999 merger between two large insurers, Aetna and Prudential, found that premiums rose by seven percentage points. Another study in the American Journal of Health Economics found that having more insurers in the marketplaces set up by the Affordable Care Act brought the cost of premiums down.
The Cigna-Anthem deal has been rumored for months, and Cigna publicly spurned Anthem's first offer in June, rejecting an offer of $184 per share.