Fast Retailing Co. has applied for approval to open stores in India, amid a push by Asia's largest clothing chain to increase its footprint across the globe.

The Japanese company submitted an application on Tuesday and seeks to do business in the country under the Uniqlo brand name, according to a filing on India's Department of Industrial Policy & Promotion website.

"India is a market with great potential," Pei-Chi Tung, a spokeswoman for Fast Retailing, wrote in an email. "At the moment, we are awaiting word from the government, and we will be able to discuss potential future steps at a later date."