NEW DELHI, Dec 22 (Reuters) - India, the world's second-biggest producer and exporter of cotton, will reopen registration for cotton exports from next week, Trade Secretary Rahul Khullar said on Wednesday. India will still allow exports of 2.5 million bales in 2010/11 despite expiry of a Dec. 15 deadline, Trade Minister Anand Sharma said on Tuesday. India is likely to produce more than 32.5 million bales of cotton in 2010/11, topping last year's 29.5 million bales, industry and government officials have said. (1 bale = 170 kg)