An announcement of a deal could come within 30 days, the sources added.
"The deal talk is around $14,000/acre," Jefferies & Co. analyst Subash Chandra said. "The devil's in the details, but the headline is likely to look good."
Spokesmen for both Reliance and Chesapeake declined to comment.
A deal with Chesapeake would be the fourth for Reliance involving US natural gas shale and its second in the Eagle Ford play.
Reliance in July said it had entered into a $1.35 billion joint venture in the Eagle Ford play with Pioneer Natural Resources and its partner Newpek, under which it obtained a 45% stake in about 212,000 net acres.
Chesapeake has been shopping for a JV partner at its Eagle Ford acreage and CEO Aubrey McClendon said in August that a deal was imminent. Chesapeake holds some 550,000 net acres in Eagle Ford.
Reliance, India's largest private company, began its shale-buying spree in April when it acquired about a 40% interest in Pittsburgh-based Atlas for about 120,000 net acres in Marcellus Shale in southwest Pennsylvania for $1.7 billion.
In early August, Reliance entered into a 60:40 JV with Carrizo Oil & Gas in the Marcellus Shale for $392 million.
China Chemical Weekly: http://news.chemnet.com/en/detail-1411716.html
