By Dana Mattioli 

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.

Cigna publicly rejected the previous offer, calling it "inadequate and not in the best interests of Cigna's shareholders." Shares of Cigna, which is based in Bloomfield, Conn., closed Wednesday at $162 each. The company's market capitalization is around $42.6 billion. That is just below Anthem's market value of $43.6 billion.

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.

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. The effort came to a head on a June Saturday when Anthem disclosed a series of bids that month, including, most recently at $184 a share. Anthem made the offers public to appeal to Cigna shareholders in the hopes they would force the company to do a deal.

Write to Dana Mattioli at dana.mattioli@wsj.com

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