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Charter Communications is preparing to make an offer of less than $135 a share for Time Warner Cable, according to people briefed on the matter.

The offer, which is likely to come in the form of a so-called bearhug letter, will consist of a mix of cash and Charter stock, setting in motion a new round of consolidation in the cable-operator industry.

Such a deal would have an equity value of around $38 billion. Charter could make its offer as early as next week.

Charter has been vocal about its appetite for a deal with Time Warner Cable, the second-largest cable operator after Comcast. In recent months, as speculation about a deal has increased, Time Warner Cable’s stock has surged from around $94 per share to as high as $138.22 per share.

On Friday afternoon, shares were trading around $131 apiece, up more than 8 percent since early September. Charter believes it can get away with offering a small premium above the current trading price because of the steep run up in recent months.

Behind the scenes, media mogul John Malone — who once sold the country’s largest cable operator, TCI, to AT&T — earlier this year acquired 27 percent of Charter through his holding company, Liberty Media. Now Malone and Liberty Media’s chief executive, Greg Maffei, are encouraging Charter to make a bid for Time Warner Cable.

Though Charter would have to take on significant debt to pay for Time Warner Cable, people familiar with the company’s thinking believe it is a manageable amount, and the combined company could pay it down quickly. Time Warner Cable does not currently have much leverage and could support a larger debt load, they said.

Time Warner Cable, however, appears in no rush to do a deal. Though its pay-television subscribers are falling, it continues to find success providing high-speed Internet and business services.

Earlier this year, Time Warner Cable approached Comcast about a merger, and Comcast appears to be taking the invitation seriously. Comcast has hired JPMorgan to advise it, a move that also gives it access to one of Wall Street’s biggest balance sheets. Such a deal would unite the two largest cable operators and face close antitrust scrutiny.

Charter’s plan to make a bearhug offer was reported earlier by Bloomberg News. All parties involved declined to comment.