(Bloomberg) -- A consortium backed by South African billionaire Johann Rupert is preparing a higher takeover bid for Mediclinic International Plc, the country’s largest hospital operator, people with knowledge of the matter said. 

Rupert’s investment vehicle Remgro Ltd. and MSC Mediterranean Shipping Co. are discussing an increase to their offer for Mediclinic, the people said, asking not to be identified because the information is private. 

The investor group is negotiating with Mediclinic’s board and may seek an extension to the bid deadline if they need more time to reach an agreement on terms, according to the people. The suitors must announce by Thursday whether they have firm plans for a bid or will walk away, unless they get an extension. 

Mediclinic last month rejected their offer of 463 pence per share, which values the company at about £3.4 billion ($4.1 billion). Shares of Mediclinic gained 0.9% to 442.20 pence at the close Wednesday in London. 

Remgro already owns nearly 45% of Mediclinic, according to data compiled by Bloomberg. There’s no certainty the investor group will proceed with a takeover, and the negotiations could still fall apart at the last minute, the people said. 

Representatives for the consortium and Mediclinic declined to comment. 

Rupert is South Africa’s richest person with a net worth of about $8.7 billion, according to the Bloomberg Billionaires Index. Through a family trust, he controls Richemont, the Swiss luxury-goods company behind brands like Cartier, Montblanc and Vacheron Constantin. 

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