Cigna shares spiked after the report, touching a new all-time high before retreating slightly. The stock was up more than 13 percent midday Monday. Months of discussions have taken place, and Anthem has made two bids for Cigna, the most recent at about $175 per share, according to the newspaper.
The news comes after reports of wider consolidation in the sector. Humana—a key player in Medicare—has received takeover interest from companies including Cigna and Aetna, the Journal reported last month.
On Monday morning, Anthem's market capitalization was about $43 billion, while Cigna's was at roughly $35 billion. Cigna's value would reach nearly $45 billion at the reported $175 per share price.
Both Anthem and Cigna told CNBC they did not comment on speculation.