Time Warner Cable, whose top executive, Glenn A. Britt, is retiring at the end of 2013, was hurt this year by TV subscriber defections during a dispute with CBS Corp. over the price of its channels.
A deal, particularly one in which Comcast acquired all of Charter, could face significant regulatory obstacles in Washington.
"The FCC would be concerned that Comcast would have de facto control over what would be available on television," Craig Moffett, one of the nation's leading telecom analysts, told Bloomberg News. "If a programmer couldn't cut a deal with Comcast, they wouldn't exist."
Comcast officials have said this year they were not interested in more cable deals. Then CNBC, the business cable channel owned by Comcast, reported on Friday that Comcast was mulling a Time Warner deal.
Comcast spokesman John Demming declined to comment. Time Warner Cable spokesman Bobby Amirshahi also declined comment. Spokeswoman Anita Lamont said Charter had no comment.
Cable stock jumped on the speculation. Time Warner shares soared 10 percent, or $12.06, to $132.92. Comcast shares shot up 4.4 percent, or $2.07, to $49.52. Charter shares rose 6 percent to $134.66.
A deal involving Comcast seemed to be favored among institutional investors.
Time Warner Cable shareholders are concerned about debt that Charter would require to purchase all of Time Warner by itself. Charter has a stock-market value of $13.5 billion and would be purchasing a cable company with a stock-market value of $37 billion.
Comcast, with deep financial resources and a diversified business, has a stock-market value of $128 billion.
Laura Martin, senior analyst with Needham & Co., said the top executives at Comcast and Charter, Neil Smit and Tom Rutledge, "are the two best operators in the cable business and a deal could be awesome as long as they share some of the upside potential with Time Warner shareholders."
In 2009, a federal appeals court overturned a regulation that would prevent a cable company from controlling more than 30 percent of the nation's pay-TV business. Kevin Martin, then chairman of the Federal Communications Commission and a Comcast critic, had adopted the measure.
Time Warner Cable has 11.4 million TV subscribers and Comcast 21 million. There are about 100 million pay-TV households in the nation.
Some believed that the 2009 court action cleared the way for Comcast to acquire Time Warner Cable or Charter. Instead, Comcast bought entertainment and news giant NBCUniversal from General Electric.