The Dolan family is preparing another run at buying the cable-television company they founded in the 1970s, offering about $10.5 billion this time, several newspapers report this morning.

Cablevision says it serves about 3 million households in the New York area, and also owns Madison Square Garden, Radio City Music Hall, the New York Knicks basketball team, the New York Rangers hockey team and several cable channels.

Two years ago, chairman Charles Dolan and his son and chief executive James Dolan first tried in vain to take Cablevision private after proposing to split off the cable system from the rest of the company.

They came back last October, offering $27 per share, but a special committee of the company’s board rejected the price as too low. The Dolans came back with an offer of $30 per share, but were again rejected.

The current offer is for $36 a share, 10 percent above Cablevision’s price at the close of trading on Tuesday.

The Financial Times notes that at that price, the Dolans would be offering more than $5,000 per subscriber, which it characterized as an unusually high price. But, it added, Cablevision can command a premium because it serves one of the wealthiest regions of the U.S.

There are problems, however. the Wall Street Journal reports that Verizon is rolling out high-speed internet and video on demand services in Cablevision’s territory. Cablevision has responded by offering internet-based phone service but now faces competition on that front from internet phone companies like Vonage.

Cablevision also faces regulatory hurdles and recently appealed a federal-court ruling that blocked its rollout of a next-generation digital video-recorder service, the Journal adds. Cablevision claims the U.S. District Court ruling in New York last month misapplied copyright law to its remote-storage digital video recorder.