Updated from 4:57 p.m. EDT

After his forays into

Mylan Labs

(MYL) - Get Report

,

Kerr-McGee

(KMG)

and

Blockbuster

( BBI), is activist investor Carl Icahn preparing to storm the towers at

Time Warner

(TWX)

?

Shares of the media conglomerate caught fire Tuesday in heavy volume after a television report said Icahn wants to put together a group of investors, possibly including Ted Turner, to force a breakup of the New York-based media empire.

The shares closed up 57 cents, or 3.2%, to $18.54 after

CNBC

reported that Icahn, the onetime corporate raider, was speaking to a number of institutional investors about Time Warner. Icahn's last high-profile move resulted in a shakeup in the boardroom at Blockbuster, the movie rental chain whose second quarter earnings report disappointed Wall Street earlier Tuesday.

Trading volume in shares of Time Warner was 40 million shares Tuesday, about twice the daily average.

Susan Duffy, a spokeswoman with Time Warner, said the company would not comment on the report, except to say the company's "management is doing everything they can to create shareholder value."

Icahn was not immediately available for comment.

Rumors have repeatedly circulated that Icahn, whose bruising proxy wars with Mylan and Kerr-McGee forced shareholder-friendly actions this year, was raising his stake in Time Warner.

"These rumors started on Friday in the options market, but I still haven't heard any confirming information," said Harold Vogel, analyst with Vogel Capital Management. "It could be a big positive for Time Warner, but we'll have to see if it plays out. Time Warner didn't have a great quarter, but for the long-term, I think they've been doing respectively well."

On Friday, the shares ran up more than 3% in double the normal volume on such a rumor. Icahn currently owns about 5 million Time Warner shares. He disclosed the stake along with several others in May.

American Technology Research analyst Rob Sanderson said he would be surprised by a move from Icahn since there are already signs that Time Warner is girding up for some sort of break-upon its own.

"They are breaking up the company," Sanderson said. "They're spinning off Time Warner Cable as soon as they can, so they are thinking along the lines of breaking things up."