– Aetna Inc., the second-largest U.S. health insurer by market value, is closing in on an acquisition of Humana Inc. and could reach a deal as early as this weekend, several people with knowledge of the matter said.

Discussions between the two companies have intensified during recent days, after it emerged over the weekend that rivals Anthem and Cigna had held merger talks of their own, said the people, who asked not to be identified discussing private information.

Aetna made a formal bid this week in the form of cash and stock, the people said. While the exact offer details weren’t available, any proposal would probably value Humana above its $28 billion market capitalization. Humana has received two offers, one from Aetna and another from Cigna, said another person. The Humana board prefers the offer from Aetna, the person said.

No agreement has been reached, the people cautioned, adding that Humana could still agree to a different transaction, such as selling itself to Anthem or Cigna, both of which have previously expressed interest. UnitedHealth Group Inc. of Minnetonka, the largest U.S. health insurer, could also make a bid for Aetna, complicating the situation even further.

The U.S. health insurance sector is undergoing a period of intense deal activity, with the five largest insurers all working either to sell themselves or buy a rival.

A representative for Humana didn’t respond to requests for comment. Representatives for Aetna and Cigna declined to comment.

Humana’s 3.2 million Medicare Advantage members have made it a target, as more Americans turn 65 and become eligible for the health program for the elderly and its private insurer-run version.

“Medicare Advantage is a coveted space,” Michael Bernstein, a partner at Baird Capital’s U.S. private equity team who focuses on health care, said in an interview. “To develop a similar scale in Medicare would take a great deal of work and time, which would be bypassed by making that transaction happen.”

Medicare Advantage membership is expected to rise to 68.4 million in 2023, up 26 percent from this year, according to the Centers for Medicare & Medicaid Services. Humana, based in Louisville, Ky., insures more than 14 million people.