The Journal said, citing the sources, that Nexstar, Irving, Texas, is the largest U.S. broadcaster and a major owner of affiliates of CW Network.
The most likely outcome would be Nexstar taking control of CW, with CBS and WarnerMedia retaining minority holdings and being the primary suppliers of programming for the network, the people told the paper.
The talks are advanced and an agreement could come soon but still might not come at all, the Journal reported.
Other suitors are out there, but the Nexstar talks are the most advanced, the people told the paper.
CW Network by itself is not profitable, but the content produced for it is valuable for other platforms at the two parents, the Journal reported.
Popular shows on CW include "Walker," "Riverdale," "All American" and "The Flash," the Journal reported.
At last check Nexstar shares were 1.9% higher at $152.
More than 30 congressional Democrats last month signed a letter sent to Attorney General Merrick Garland and Justice Department antitrust chief Jonathan Kanter, calling for an investigation into the pending $43 billion merger of Discovery and AT&T-owned WarnerMedia.
The merger between the two companies was first announced last May.