In a move that could lead cable operator Insight Communications to follow the path taken by Cox Communications, Insight co-founders Stanley Knafel and Michael Willner and the private-equity firm The Carlyle Group on Monday announced a $650 million proposal to take the company private.

As part of the plan, Mr. Knafel, Insight’s chairman, Mr. Willner, Insight’s CEO, and The Carlyle Group will form an acquiring entity called New Insight LLC that would offer to purchase all outstanding Insight shares for $10.70 apiece, representing an 11 percent premium over Insight’s March 4 closing price. Mr. Knafel and Mr. Willner combined own around 14 percent of Insight’s equity and control 62 percent of the stock vote.

The transaction would put Insight’s enterprise value at around $2.1 billion, and, if approved by independent directors and shareholders, would keep Mr. Knafel, Mr. Willner and the rest of the management team in place, the company said.

The move to go private is generally being seen by Wall Street analysts as an indication of Mr. Knafel and Mr. Willner’s confidence in the cable business, and perhaps their frustration at Insight’s weak stock price. Insight has about 1.3 million subscribers in Illinois, Indiana, Kentucky and Ohio.

If Insight’s shareholders approve the plan, Insight will be the second cable company to go private in the span of a year. Cox Communications did so in 2004 after controlling shareholder Cox Enterprises acquired the 38 percent of Cox Communications it didn’t already own for $8.5 billion.