(MarketWatch) SÃO PAULO—At least two groups are proceeding with plans to bid for Brazil’s second-largest provider of medical diagnostics, in what could be the second major deal this week in an industry where investors spy potential growth and profits.

Consortiums led by JP Morgan Chase & Co.’s Gávea Investimentos Ltda and Blackstone Group LP are looking to buy out a group of doctors that own 41.2% of Fleury SA in a deal that could be worth some $500 million based on current market prices, according to people familiar with the talks. The people said there may be other bidders in the running.

Gávea and Blackstone declined to comment.

All of the potential buyers had to make preliminary offers over the last 40 days for the doctors’ stake in the company, one of those people said. On Thursday, Fleury said in a statement that it had been notified bids for the shares have been received but didn’t provide further details.

The prospect of the deal, which has been in the works for some time, follows billionaire businessman Edson Bueno’s $747 million purchase Monday of a majority stake in the No. 1 player in the sector, Diagnósticos da America SA.

Shares of Fleury are up 3% this week to 18.69 Brazilian reais on speculation about a possible sale. Over the last 12 months, its shares have declined about 15%, while the Ibovespa stocks index has lost 17%.

Analysts point to rising prosperity in Brazil, particularly for an up-and-coming middle class, as the main driver for the Brazilian health industry. Currently, around 25% of Brazilians use private health care, and this could increase to 30% by 2017, according to Fitch Ratings. On the downside, the diagnostics sector faces significant pressure from high inflation, mostly related to medical fees and rents.

According to Thomas Chang, an analyst at the UM Investimentos brokerage in São Paulo, the value of medical-testing companies in Brazil has fallen as a result of weaker-than-expected economic growth, but prospects remain decent as private health care is still relatively small and Brazil’s populations is getting older.

“Only 25% of the population has private health insurance—you can compare it to 50% in Mexico and to 75% in the U.S.,” Mr. Chang said.

Brazilian shares have become even more attractive thanks to the depreciation of the Brazilian real against the dollar. The real has plunged 35% against the dollar over the last three years—a move that accelerated last year as the U.S. Federal Reserve began to indicate that it would start to reduce its easy-money policies.

In mid-November, the group of doctors that control Fleury’s shares hired JP Morgan to seek alternatives for Core Participações SA, a holding company that owns a controlling stake in Fleury.

Core owns 41.2% of Fleury, directly and indirectly. Core controls Fleury through a partnership with the health-insurance arm of Banco Bradesco SA, which owns 16.4% of Fleury.

Fleury posted revenue of 1.6 billion reais ($666 million) in the 12 months ended September 2013. The company, founded in 1926, has a market value of 2.8 billion reais, suggesting Core’s stake would be worth around $500 million. Because the sale of Core implies a change in the controlling group at Fleury, it likely would trigger a tag-along offer that could cost another $500 million, according to a person familiar with the transaction.

The Carlyle Group CG +1.56% LP, which also held talks with JP Morgan regarding Fleury, lost interest because the tag-along rights would make the deal too expensive, a person familiar with the sale said. A spokeswoman for Carlyle said the company doesn’t comment on market rumors.

Gávea Investimentos, created by former central bank president Arminio Fraga, wants to pair up with another fund to buy the stake, a person familiar with the talks said. Gávea already owns 30% of a local diagnostics firm called Hermes Pardini, based in the state of Minas Gerais.