By Dana Mattioli And Anna Wilde Mathews 

Health insurers Anthem Inc. and Cigna Corp. are in talks to combine after Cigna last month spurned a $47.5 billion takeover from Anthem, according to a person familiar with the matter.

Representatives of the companies met Friday and Tuesday to discuss a potential tie-up, the person said. A deal could be reached in coming weeks, the person said, though there is no guarantee the latest round of talks will result in a tie-up.

Anthem has been trying to combine with Cigna for nearly a year, but the two companies have struggled to agree on price and other terms, including who would run the combined company. Last month, in an attempt to woo Cigna shareholders, Anthem made public its most recent offer of $184 a share.

The talks come amid a flurry of discussions among the top five health insurers aimed at striking deals that will enable them to be more competitive in a health-care landscape dramatically altered by the Affordable Care Act and other developments.

Even amid the Anthem talks, Cigna continues to examine a potential purchase of Louisville, Ky.-based Humana Inc., people familiar with the matter said. In that potential tie-up, it is vying with Aetna Inc., which has made a takeover proposal for Humana. Aetna, meanwhile, has been stalked by UnitedHealth Group Inc., the largest health insurer, according to people familiar with the matter.

The talks come as a smaller managed-care company, Centene Corp. agreed to buy Health Net Inc. for around $6.3 billion in cash and stock--unexpectedly scoring the industry's first deal after weeks of circling among bigger health insurers.

The combination gives Centene, based in St. Louis and largely focused on Medicaid, a major presence in California, Health Net's home turf. It also appears to remove from the merger equation two smaller players that had long been seen as potential acquisition targets for the biggest companies.

As for Anthem and Cigna, the two companies have clashed--among other things--over the role Cigna Chief Executive David Cordani would play in a combined company. He wants to be CEO, if not immediately then after some time, which Anthem refuses to guarantee.

Anthem, based in Indianapolis and until last year known as WellPoint, is a huge player in the individual and small-group markets in the 14 states where it holds the rights to be the Blue Cross and Blue Shield insurer. It also has a strong role among national employers.

Cigna focuses closely on self-insured commercial business and has a significant and growing position overseas. Combining the two would create a big competitor in the commercial health-insurance business, with strong positions among individual, small-business and big-employer clients.

At Friday's meeting, Anthem and Cigna discussed potential synergies if the two companies were to combine, said one of the people. Another issue discussed, the person said, was Anthem's role as a Blue Cross and Blue Shield insurer, an issue Cigna also highlighted in a letter to Anthem that it made public. The Blue Cross and Blue Shield plans hold geographic rights to use the Blue brand only in a particular area, and they also agree to certain limits on their non-Blue business.

It is unclear how Anthem would manage the legacy Cigna business in states where another insurer is the local Blue. In its letter, Anthem said it was "confident in its ability to obtain regulatory approvals" and this "includes matters related to the Blue Cross Blue Shield Association."

Cigna countered by highlighting potential complications arising from Anthem's affiliation with the Blue system, including litigation against it.

Shares of Cigna, which is based in Bloomfield, Conn., closed Wednesday at $162 each. The company's market capitalization is around $42.6 billion, just below Anthem's market value of $43.6 billion.

Thursday, shares of Cigna rose 0.2% in midday trading, while Anthem shares slipped 1.5%.

Centene, meanwhile, said it expected significant synergies from its deal for Health Net, amounting to $150 million a year by the second year. Centene said the combined company would have pro forma revenue of around $37 billion for this year. The deal values Health Net shares at around $78.57, a 21% premium over Health Net shares' closing price on July 1.

For Centene, the deal brings a major presence in California's Medicaid, the nation's largest version of the program for lower-income Americans, where it had only a limited role before. It also lands Centene in the state's program to manage beneficiaries who qualify for both Medicaid and Medicare, known as dual eligibles. These populations have been seen as a huge opportunity for managed-care companies but also a big challenge, because of their complexity and often significant health needs. In California and other places, some companies have struggled with dual beneficiaries choosing to opt-out of their programs.

Health Net's California Medicaid business is particularly low-risk, because of a legal settlement with the state that guarantees a margin of 3.255%, said Sarah James, an analyst with Wedbush Securities. The two companies may potentially benefit from jumping sooner than other insurers considering combinations, she said, as Justice Department regulators appear to be signaling they will likely review an expected spate of industry deals in a way that considers their combined impact on competition.

"There could be an advantage to being at the earlier end of it," the analyst said.

Write to Dana Mattioli at dana.mattioli@wsj.com and Anna Wilde Mathews at anna.mathews@wsj.com

Corrections & Amplifications

An earlier version incorrectly said Humana had the smallest revenue total among the top five health insurers.

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