BENGALURU, Sept 25 (Reuters) - India's billionaire Burman family said on Monday it would buy around 26% of Religare Enterprises for 21.16 billion rupees ($255 million), as it seeks to bolster its presence in the rapidly growing financial services sector.

The Burmans, who founded consumer goods conglomerate Dabur India and are worth around $10 billion according to the Forbes India Rich List, are already the biggest single shareholder in Religare with around a 21% stake.

The Burmans now want to "increase the family's stake and take control" of Religare, in a move that will pit them against other billionaire families in the same business, including Mukesh Ambani's Jio Financial Services and family-controlled Bajaj Finance.

"The proposed transaction is in line with our vision to create a leading financial services platform that encompasses lending, broking and health insurance services," Anand Burman, Dabur India chairman emeritus, said in a statement.

With India's economy booming, demand for loans have been on the rise, pushing companies like Bajaj Finance, Tata Capital and Aditya Birla Capital to raise fresh funds.

Earlier this year, Reliance Industries spun off Jio Financial Services into a separate unit to better compete with its rivals.

"India's financial services space is still under-penetrated, and big family groups and conglomerates want a bigger piece of the pie," said Anand Dama, BFSI head at brokerage firm Emkay Global.

Shares in Religare, which provides loans to small and mid-sized businesses, and also has health insurance and broking services units, fell as much as 6.9% on Monday.

The Burmans are offering to buy 90 million shares at 235 rupees per share, the offer document shows, a sharp discount to the stock's last closing price of 271.55 rupees.

The Burmans reserve the right to appoint directors to Religare's board and make changes in the management structure as determined by its board, the offer document shows. (Reporting by Sethuraman NR in Bengaluru, Aditya Kalra in New Delhi, Praveen Paramasivam in Chennai and M. Sriram in Mumbai; Editing by Sohini Goswami and Sharon Singleton)