A Time Warner spokesman would not confirm reports Britt would step down at the end of the year.
"Glenn Britt is currently under contract with Time Warner Cable. If and when that changes we will announce it," the spokesman said.
The Journal reported Saturday that Britt's contract with the company he has led since 2001 expires at the end of the year.
Industry analyst Vijay Jayant at ISI Group LLC said Britt had done "a fantastic job on the equity broadly, which the stock price shows."
Britt has supported investor confidence with stock buybacks and dividends, the Journal said. But stock values are still down due to escalating subscriber losses in 2012.
There is "still no evidence of operating momentum," at Time Warner -- the fourth-largest U.S. television service -- said Michael Senno, an business analyst at Credit Suisse.
Britt's likely successor is Rob Marcus, Time Warner's president and chief operating officer, the Journal reported.
Britt took the top job at Time Warner in 2001. His departure comes during a turning point the industry, with production costs rising and the Internet presenting a rival in a world of quickly evolving technologies.