NMC, which joined the London Stock Exchange in 2012 and was promoted to the blue chip FTSE 100 index in 2017, operates clinics and hospitals, specialized maternity and fertility clinics, and long-term care homes hospitals across 19 countries.
But it has lost more than two-thirds of its value since U.S.-based short-seller Muddy Waters questioned its financial statements in December, prompting major shareholders to sell out.
"Today's bizarre disclosures about even more pledges and debt validate that the cockroach theory is alive and well - what we found is likely just the tip of the iceberg," Muddy Waters' Carson Block said in a statement.
"As for the notion that NMC might receive private equity bids, it's hard for us to believe they would survive due diligence," he added.
NMC declined to comment on the short-seller's statement.
However, earlier NMC said: "The Company's operations continue to perform strongly, and the Company expects to report full-year 2019 results in-line with management's expectations."
Former FBI boss Louis Freeh is leading a separate independent review committee appointed by London-listed NMC to investigate the Muddy Waters allegations.
NMC said it has not had talks on the terms of any potential offer. KKR declined to comment, while GK could not be reached.
"Just when you thought it couldn't get any stranger with NMC Health, there are two new twists in the tale of the troubled hospital operator...Taking the business private might be the best thing to happen to NMC as it has lost credibility with the market and it will take a lot to rebuild trust with investors," Russ Mould, investment director at AJ Bell, said.
NMC shares were up 6.7% at 747.2 pence at 1327 GMT.
NMC said the ongoing review into inaccurate disclosures in the past would also affect the interests of two other major NMC shareholders, vice-chair Khaleefa Al Muhairi and Saeed Al Qebaisi.
Based on the initial probe, the Indian billionaire's stake in NMC will likely come down by 9.58%, NMC said. A spokesman for NMC declined further comment.
Shetty owned 19.22% stake as of May last year, while NMC vice-chair Muhairi and Qebaisi had 15.82% and 7.66%, respectively, as of Jan. 28, Refinitiv data showed.
Muhairi and Qebaisi also sold some shares in NMC and Finablr last month. The payments firm is also co-chaired by Shetty.
Finablr on Monday said that independent directors were reviewing arrangements between Shetty and the two shareholders and it could impact its shareholding structure.
Shetty had pledged over half of Finablr's stock as security against debts it incurred in buying Travelex, the company disclosed last month. He owned nearly 63% of Finablr as of August.
Finablr shares, also hit by the Muddy Waters allegations against NMC, were up 7.7% at 77.05 pence.
(Reporting by Pushkala Aripaka in Bengaluru, Iain Withers in London and Saeed Azhar in Dubai Editing by Arun Koyyur and Alexander Smith) ((Pushkala.A@thomsonreuters.com; Twitter: @pullthekart; within UK: +44 20 7542 1810, outside UK: +91 80 6749 6633;))