Other hospital chains that have been exploring a potential deal include HCA Holdings Inc and LifePoint Hospitals Inc, some of the people said. They asked not to be named because the matter is not public.

News of the takeover interest comes as Health Management seeks to fend off a campaign from hedge fund Glenview Capital Management, which has threatened to launch a proxy battle against the company.

Shares of Naples, Florida-based Health Management rose 8.3 percent to $16.75 on the New York Stock Exchange on Tuesday, valuing the company at over $4.3 billion.

Shares of Community Health, which several sources familiar with the matter have identified as the most likely buyer, rose 4.1 percent to $48, giving it a market value of around $4.5 billion.

Representatives for Health Management, HCA and LifePoint declined to comment. Community Health did not immediately respond to requests for comment.

Since President Barack Obama's healthcare reform was passed in 2010, there has been a wave of consolidation - more than 650 deals for hospitals, according to Thomson Reuters data - as hospital operators seek to protect themselves against increasing costs and lower reimbursement fees from the government.

On June 24, Tenet Healthcare Corp announced a deal to buy smaller rival Vanguard Health Systems Inc for $1.73 billion, putting it in a better position to benefit from the millions of Americans about to get insurance under Obama's healthcare reform.

The combined company will be the second-largest for-profit U.S. hospital operator, with total revenue of about $15 billion in 2012, behind HCA but surpassing Community. Tenet fended off a hostile takeover effort from Community Health in 2011.

Health Management said last month it hired Morgan Stanley and law firm Weil, Gotshal & Manges in response to Glenview's campaign.

Glenview in a letter to Health Management shareholders last month said there was "significant room for improvement," saying that the company "for over a decade ... has fallen short in their financial returns." Glenview said it holds a 14.6 percent stake in Health Management.

The company said on May 28 that Chief Executive Gary Newsome would retire at the end of July and its board of directors had begun a search for his replacement.

A Community-Health Management combination would preserve Community's rank as the second-largest for-profit U.S. hospital operator, behind HCA. On its own, Community will drop to No. 3 when Tenet completes its acquisition of Vanguard.

Community and Health Management both operate hospitals in smaller cities and rural areas, with some overlap in markets in the U.S. Southeast, said CRT Capital Group analyst Sheryl Skolnick.

In comparison, HCA focuses on larger markets, while LifePoint in recent years has been quiet on the acquisition front, analysts said.

"Community has shown an appetite to make a big acquisition," said Les Funtleyder, healthcare strategist at investment firm Poliwogg.

But even if Health Management's stock pulled back to $15 a share from current trading levels, the company still would be an expensive purchase for Community and might not generate enough cost savings to justify a deal, Skolnick said.

(Reporting by Soyoung Kim, Jessica Toonkel and Greg Roumeliotis in New York; additional reporting by Susan Kelly in Chicago; editing by Gerald E. McCormick and Leslie Adler)

By Soyoung Kim, Jessica Toonkel and Greg Roumeliotis