The company has held talks with advisers and potential buyers, Bloomberg reported on Wednesday, citing people familiar with the matter. (http://bloom.bg/1W9bWec)
Chesapeake was not immediately available for comment.
The company said last month that it planned to sell assets worth $500 million to $1 billion this year to reduce debt.
Asked if Stack shale assets were among those marked for sale, Chief Executive Doug Lawler had then said on a post-earnings call that the company did not have any current plans, but he had not ruled it out.
The Stack shale assets Chesapeake is considering selling could fetch $300 million-$700 million, Bloomberg reported, citing one of the people.
Chesapeake's shares were up about 7 percent at $4.61 in afternoon trading on Wednesday, mirroring a broad rally in oil and gas stocks due to higher crude prices.
(Reporting by Amrutha Gayathri and Vishaka George in Bengaluru; Editing by Kirti Pandey)