The stock was among the top gainers on India's NSE index, rising as much as 8.22 percent in early trade to 401.40 rupees, the highest since August 2011.
Modi wants to fix India's inefficient coal sector quickly to improve electricity supply across the country. Coal generates more than half of the country's power and is the cheapest form of energy.
Sources said any reform will begin with Coal India, which accounts for 80 percent of India's total coal output but has failed to meet its output targets for years.
Red tape, strikes, protests against land acquisition and delays in obtaining environmental approvals have kept coal output far below demand, making India the world's No.3 importer even though it sits on the fifth-largest reserves.