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(Reuters) - Time Warner Cable would rather grow through acquisitions than be bought by billionaire John Malone, and has been eyeing Cablevision, its most coveted target, and No. 3 cable operator Cox Cable, according to three people familiar with Time Warner Cable's thinking.

Time Warner, the second-largest U.S. cable operator with more than 12 million subscribers, has contacted both companies in recent months to discuss options including a merger, according to one of the people, although in neither case have the talks progressed to any serious consideration of a transaction. The source did not say how recent the talks were.

New York-based Cablevision, the No. 5 cable operator, and Georgia-based Cox are controlled by families that have so far shown no interest in selling, according to the people familiar with the matter.

Cablevision's founding Dolan family controls 72.9 percent of the company's stock, according to its proxy statement. Privately held Cox Enterprises is also family-controlled.

Malone, whose Liberty Media owns a 27 percent stake in cable operator Charter Communications, is working out options to acquire Time Warner Cable, according to published reports.

Time Warner Cable Chief Executive Glenn Britt is not interested in a Charter merger, according to people with knowledge of the matter.

Since cable pioneer Malone jumped backed into the U.S. cable market with Liberty Media's investment in Charter earlier this year, analysts have predicted a wave of cable consolidation. The U.S. cable TV market is mature and faces rising programming costs.

A fourth person familiar with Time Warner Cable's thinking said that its executives believe a merger with Charter would not benefit Time Warner Cable shareholders because of the large amount of debt it would put on the combined company's balance sheet. They are also sceptical about potential synergies.

The person, who asked not to be named because he was not authorized to speak with the media, said Charter's purchase of the company was a "far fetched notion" that would not appeal to Time Warner Cable's shareholders.

Representatives for Time Warner Cable, Cox and Cablevision declined to comment.

Time Warner Cable's management is more interested in being an industry consolidator, the people say. Cablevision has 3.2 million densely clustered subscribers in the New York metropolitan area, the company said in its most recent earnings statement. That could fit well with Time Warner's New York systems.

Cablevision also has a high-income subscriber base that is viewed as attractive by rival cable companies.

Brean Murray analyst Todd Mitchell said that Cablevision and Time Warner Cable have neighbouring cable systems and because their markets do not overlap, there would not be any regulatory issues in a potential tie-up.

Cox, which has 4.5 million subscribers, is also attractive to Time Warner Cable, because it has large holdings on the West Coast, including in southern California, where both companies have neighbouring systems. Time Warner Cable has spent billions of dollars on local sports rights for the Los Angeles Dodgers baseball team and the Los Angeles Lakers basketball team, and it could tap into Cox's markets with those channels, Mitchell said.

Cablevision, which the Dolan family unsuccessfully tried to take private in 2007, has been grappling with increased competition from rival Verizon FiOs in its main footholds in Long Island, New Jersey and Connecticut, and is losing video customers. Analysts say that Cablevision would now be less likely to go private because of its high debt ratio and lower cash flow.

Family patriarch Chuck Dolan, the founder and chairman of Cablevision, who is 86, might be more in the selling mood than he was been before, said one person familiar with the company.

"They don't want to be in it long term anymore," said the person.

Cablevision is a "good asset and would be of interest to Time Warner Cable," as well as other companies, the person said.

(Additional reporting by Soyoung Kim; Editing by Peter Henderson and Steve Orlofsky)