Shares of Dynegy jumped to close up about 17 percent at $10.78. Vistra Energy ended trading at $20.32, up 3.8 percent.
Talks to combine the two energy companies, reportedly in the works since May, could lead to a deal being officially announced as soon as next week, according to the Journal. It would mark further consolidation among independent power producers, the companies that generate electric power and sell it into wholesale markets.
The two companies' combined enterprise value, a more comprehensive measure of total value than market capitalization, would value the merger at more than $20 billion, the Journal reported.
Neither company immediately responded to CNBC's request for comment.
The purchase would help Vistra expand into the Midwest and Northeast, where Dynegy operates a number of natural gas and coal-fired plants.
In addition to generating power, Dynegy and Vistra both play in the retail electricity space, which sells power to residences and businesses. That business typically does well when power prices are low, like they are now. The power generation side usually suffers when prices are soft.
Independent power producers have struggled to find a winning business model since a wave of deregulation in the early 2000s. The goal of deregulation was to promote competition in the utility sector and drive down power costs, but sea changes in the space have created challenges for merchant generators.
The unexpected boom in U.S. natural gas production over the last decade has pushed down power prices, making it harder for companies that operate plants to turn a profit. At the same time, subsidies and other support for renewable energy projects have boosted competition from wind and solar power and piled pressure on coal-fired and nuclear power plants.
The industry has been plagued by bankruptcies. Dynegy entered Chapter 11 bankruptcy in 2011, and Vistra itself was spun out of the bankruptcy of Energy Future Holdings, one of the largest in history.
The deal potentially takes a chess piece off the table for NRG Energy, the power producer that announced a transformation plan earlier this year under the guidance of billionaire hedge-fund manager Paul Singer and fellow activist investor Charles John Wilder.
Analysts told CNBC earlier this year that purchasing Dynegy would allow NRG to pick up a large portfolio of combined cycle plants, the most efficient type of natural gas facilities.