(Credit: Fernando Leon/Getty Images)

A future without television as we know it may be in the works, says one of the top people in the cable industry.

Cablevision president and CEO James Dolan said "there could come a day" when his media and telecommunications company stops offering television service, instead opting for broadband, according to the Wall Street Journal.

Cablevision Systems Corp. (NYSE: CVC), founded in 1973 and now the fifth-largest US cable firm, provides television, phone and Internet services to millions of people in the New York metro area, according to its website.

Dolan, 58, said that his young children prefer to watch online video service Netflix using Cablevision broadband. He has six boys, ages 4 to 26.

Dolan's comments, which come during a bitter riff between CBS and one of the largest cable providers, Time Warner Cable, are an unexpected public acknowledgement by a cable CEO about the possible shift in the television industry.

Read More: CBS, Time Warner Cable Standoff Could Last Weeks

Cable companies are increasingly facing demands for higher fees by TV programmers as it becomes harder to find new broadband customers. Meanwhile, consumers are increasingly turning to the Internet for programming. Last week, Cablevision reported total customers fell by 11,000 to 3.22 million in the second quarter.

On an average monthly basis, U.S. viewers spent an average of 8 hours 20 minutes watching video on the Internet in the first quarter of 2013, according to data from Nielsen, up from 5 hours 24 minutes watching video on the Internet in the same quarter last year.

Dolan is also chairman of The Madison Square Garden Company (NASDAQ: MSG), the sports and entertainment company that owns the home of the New York Knicks.

A spokeswoman for Cablevision declined to comment about Dolan's interview.