SAO PAULO, Aug 19 (Reuters) - Investment funds linked to businessman Nelson Tanure have bought around 26% of medical diagnostics company Alliar, he said on Thursday, complicating a proposed takeover by hospital chain Rede D'Or .

Tanure released a statement after markets closed saying he had become Alliar's biggest individual shareholder, acquiring an additional 21.14% stake on Thursday from funds managed by Patria Investments Ltd. On Wednesday, a fund linked to Tanure reported that it had built a 5.13% stake in Alliar.

He has no plans to change Alliar's management, Tanure said.

"We believe that medical diagnosis is a promising sector in Brazil," Tanure said, adding that his daughter was a physician with investments in other healthcare companies.

Shares in Alliar jumped as much as 15% after business news website Brazil Journal first reported Tanure's aggressive buying on Thursday, before trimming gains to 6% at the closing bell.

Tanure's move came after hospital chain Rede D'Or on Monday announced a tender offer to acquire Alliar for 1.36 billion reais ($252 million), paying 11.50 reais per share.

Alliar shares surged as high as 14.18 reais on Thursday afternoon before closing at 13.06 reais.

Shares of Rede D'Or, which aims to expand beyond its hospital business with the acquisition, were little changed.

Alliar and Rede D'Or did not reply to requests for comment.

($1 = 5.3877 reais) (Reporting by Carolina Mandl; additional reporting by Anthony Boadle in Brasilia; editing by Brad Haynes and Steve Orlofsky)