Speculation over a combination of the companies underscores the pressure the nation's largest wireless carrier faces to do a deal in the wake of AT&T Inc's planned $85.4 billion takeover of Time Warner Inc. Verizon and other carriers also face a saturated smartphone market.

Verizon said in July that it struck a deal to buy Yahoo Inc's core internet properties, but the deal was cast into doubt after Yahoo disclosed data breaches last year.

"I think the market is predictably impatient and wants Verizon to do something yesterday," said Craig Moffett, an analyst at MoffettNathanson. "The market inevitably draws the comparison to AT&T that, for better or worse, has made its big strategic bet."

After rising as much as 10 percent and hitting a session high of $341.50 on the news, Charter shares eased and were trading up 6.5 percent at $330.59. Verizon shares were down 1.4 percent at $49.08.

Charter and Verizon declined to comment.

A Charter acquisition would signal that Verizon has a drastically different strategic vision than rival AT&T, which has sought to diversify away from the wireless business through its deal for Time Warner and earlier acquisition of satellite-TV provider DirecTV.

Instead, a deal for Charter would indicate Verizon is betting on infrastructure. On its earnings conference call with investors on Tuesday, Chief Financial Officer Matt Ellis said that 5G wireless technology was a focus for Verizon.

"The great irony could be that the cable operators are better positioned to compete in 5G wireless than the wireless operators themselves," Moffett said.

Speculation over a tie-up with Charter has been building steadily since last month when Verizon Chief Executive Officer Lowell McAdam told Wall Street analysts that such a deal would make "industrial sense," according to a December note by BTIG analyst Walter Piecyk.

With Charter, Verizon would gain a fiber and cable network across 49 million homes, including markets in California, Texas, and Florida, that the wireless carrier recently divested to Frontier Communications Corp, JPMorgan analysts said in a note in December.

From a traditional antitrust point of view, the combination of a phone company and a cable company would not raise competition issues that cannot be overcome, said George Bittlingmayer, a professor at the University of Kansas School of Business.

"The wildcard here is whether people's unhappiness with their cable and mobile phone providers would translate into some grandstanding and arm-twisting on the part of the new administration for political benefit," he said.

Phil Cusick, an analyst at JPMorgan, said in an email on Thursday that he expects $2 billion in annual synergies from a Charter deal but added that the deal's math is "difficult to make work," noting that a combined company would be heavily leveraged. 

The Wall Street Journal, which first reported a preliminary approach between the companies, said it was unclear if Charter's executives would be open to a transaction and that there was no guarantee a deal would be struck.

Verizon had a market capitalization of $203 billion as of Wednesday's close, while Charter was valued at nearly $84 billion, according to Thomson Reuters data.

(Reporting by Anjali Athavaley in New York and Liana B. Baker in San Francisco; Editing by Jeffrey Benkoe and Alan Crosby)

By Anjali Athavaley and Liana B. Baker