SAO PAULO, Nov 19 (Reuters) - Investment funds linked to Brazilian businessman Nelson Tanure have proposed to buy a controlling stake in medical labs company Alliar, according to a securities filing late on Thursday.

Tanure offered to pay 20.50 reais per Alliar share, a 35% premium over Thursday's closing price. Under the deal terms, controlling shareholders in Alliar have up to Nov. 26 to make a decision.

The businessman announced in August he had acquired a 26% stake in Alliar, saying he believed medical diagnosis was a promising sector in Brazil and that his daughter, a physician, had other investments in the industry.

Controlling shareholders have a 52% stake in the company, which means Tanure would pay roughly 1.3 billion reais for their shares. (Reporting by Carolina Mandl Editing by Mark Potter)