By Liz Hoffman, Dana Mattioli and Anna Wilde Mathews 

Aetna Inc. is nearing a deal to buy Humana Inc., according to people familiar with the matter, in a tie-up of health insurers that could be announced this week.

The people said a deal could be inked as soon as Thursday night, though they cautioned the timing could slip.

Aetna is expected to pay about $230 a share for Humana, one of the people said. This price would value the Louisville, Ky., insurer at about $34 billion. Humana's market value was $28.9 billion as of the market close Thursday.

A takeover approach for Humana earlier this year thrust the biggest health-insurance companies into a five-way merger frenzy. Cigna Corp. and Aetna were vying to buy Humana, while trying to rebuff takeover approaches of their own. Cigna has been in talks with Anthem Inc., and UnitedHealth Group Inc. earlier approached Aetna.

A deal to buy Humana would vault Aetna toward the top of the burgeoning Medicare business and give it scale to thrive as the industry consolidates.

But expected scrutiny from antitrust regulators, along with signs of some emerging operational challenges at Humana, will put pressure on Aetna and its chief executive, Mark Bertolini, to demonstrate that the big bet will pay off.

A price of $230 per share for Humana would represent a premium of 23% from Thursday's close, and 29% from the company's share price before The Wall Street Journal in late May first reported Humana was exploring a sale.

In picking up Humana, Aetna would get a unique asset--a company with a rapidly growing Medicare enrollment that totals 3.2 million. This, combined with Aetna's Medicare membership of 1.26 million, would likely put the merged company close to current industry leader UnitedHealth.

The Medicare business is considered a growth engine for the industry, as baby boomers age into eligibility and choose the private-insurer version of the government program, known as Medicare Advantage plans.

Humana performs strongly in a key measure of Medicare quality known as star ratings, which are tied to government payments. The insurer has been moving rapidly to forge close ties with doctors and other providers in efforts to boost performance and rein in costs.

Humana is also a leading provider of Medicare drug benefits, known as Part D plans, with 18% of that market, according to a tally by Wells Fargo Securities.

A deal would have particularly high stakes for the federal government because of Humana's key role in Medicare and its significant footprint in the health law's insurance exchanges.

A Wall Street Journal analysis found that an Aetna-Humana tie-up would increase by about 180 the number of U.S. counties where at least 75% of customers for Medicare Advantage plans are in the hands of a single insurer. In eight states, an Aetna-Humana merger would remove a competitor from the exchanges in which individuals can buy coverage under the Affordable Care Act, though insurers may not offer plans in every region of a state.

Goldman Sachs health-insurance analysts, looking at potential market-concentration issues, estimated that around 13% of the combined Medicare Advantage enrollment of a combined Aetna-Humana could be at risk of divestiture if the two companies sought to merge. The analysts estimated the figure at around 18% of the combined individual-insurance business and 16% of small-group plan enrollment, though some states were excluded from those tallies.

In recent months, Humana has shown signs of operational snags.

Humana has missed analysts' earnings projections for the last three quarters. It has warned of a possible uptick in hospital utilization among its Medicare members, and it has disclosed a Justice Department probe into how Medicare Advantage insurers score the health risks of their members, which affects their payments.

Humana has also struggled with its business on the health law's marketplaces. Recently, the Obama administration released calculations of health-insurer payments for 2014 under Affordable Care Act programs designed to help insurers that enrolled a lot of sicker, costlier consumers. Humana's allotment appeared to come in significantly short of its projections. The amounts made public so far aren't complete yet, however.

A deal would be a capstone for Mr. Bertolini, as it likely ensures that Aetna will endure in an industry that many experts think could shrink soon to just three major players at the top. Aetna's revenue last year totaled $58 billion, while Humana's was $48.5 billion. The current No. 2 insurer by revenue, Anthem, had $73.9 billion, while UnitedHealth Group's was $130.5 billion, including its health-services arm, Optum.

A tie-up would turn eyes toward Cigna, which would end up considerably smaller than its peers with revenue of $34.9 billion and with a business largely focused on self-insured employers, along with a significant overseas presence.

During the last major round of insurance-industry deal making, Mr. Bertolini picked up Coventry Health Care Inc., closing that acquisition in 2013. That left Aetna with a bigger individual-insurance business, as well as increased Medicare and Medicaid, but it didn't reshape Aetna the way the Humana acquisition would, tipping a company long known for its employer business far deeper into the government space.

A deal would also mark the end of Humana as a stand-alone company. It has long been a prominent name in the health industry and a major presence in its hometown, Louisville.

Humana was once a major health-care provider, but it spun off its hospital unit in 1993. Longtime former Humana CEO Michael B. McCallister, who took over the company when it was struggling in 2000, is credited with steering it deeply and successfully into the Medicare business, which has remained at the center of the company.

Write to Liz Hoffman at liz.hoffman@wsj.com and Dana Mattioli at dana.mattioli@wsj.com

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