Charter Communications is near a deal to buy Time Warner Cable for about $55 billion, people with direct knowledge of the talks said on Monday, a takeover that would create a new powerhouse in the rapidly consolidating American cable industry.

Under the proposed terms of the deal, Charter will pay about $195 a share in cash and stock. That is roughly 14 percent higher than Time Warner Cable’s closing stock price on Friday — and 47 percent higher than Charter’s original bid for its rival from early last year.

A deal could be announced as soon as Tuesday, though these people, who were not authorized to speak publicly about private negotiations, cautioned that talks were continuing and might still fall apart.

The potential acquisition of Time Warner Cable completes a lengthy quest by Charter and its main backer, the billionaire John C. Malone, to break into the top tier of the American broadband industry.

If completed, the transaction would be the latest in a series of mergers remaking the market for broadband Internet and cable television in the United States. Just last week, the European telecommunications company Altice agreed to buy Suddenlink for about $9 billion.

And Charter is also nearing an agreement to acquire another cable operator, Bright House Networks, in a transaction that could also be announced soon.

Last year, Mr. Malone tried to penetrate the American broadband industry, but Charter was foiled by its larger rival, Comcast, which bid $45 billion for Time Warner Cable. Comcast, the country’s biggest cable operator, ultimately failed in its effort, with federal antitrust regulators believing that the merger would have been untenable.

Government regulators are also expected to closely scrutinize a combination of Charter and Time Warner Cable, according to analysts, though as a smaller transaction it may face less opposition.

Since the collapse of the Comcast agreement, Charter has worked to win over its onetime reluctant target, focusing on a friendly deal and acknowledging that it would have to pay a much higher price tag.

Yet the company may still face competition for Time Warner Cable in the form of Altice, which has ambitions to extend its telecom empire across the Atlantic, beginning with the acquisition of Suddenlink.

News of the proposed terms of a Charter deal for Time Warner Cable were reported earlier by Bloomberg News.