(FORTUNE Magazine) - Separated by three long blocks of Central Park South in Manhattan, two powerful businessmen sit in two impressive skyscrapers, all but glaring at each other across the park.

On the east side, in the old GM building, sits the investor-provocateur Carl Icahn. On the west side, in the spanking-new Time Warner Center, sits Dick Parsons, CEO of the building's No. 1 occupant.

Dick Parsons, Time Warner CEO, and Carl Icahn.

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As you surely know, Icahn (and please don't call him a corporate raider -- he hates that) is agitating for change at Time Warner (owner of FORTUNE's and CNNMoney.com's publisher). Icahn says the company is poorly managed and needs to make radical moves to get its stock to pop.

Parsons replies that he's doing everything possible to improve performance at the world's largest media company and points out that all media stocks are depressed right now.

Parsons is smooth and cool, Icahn rough and noisy -- but they have at least one thing in common: No matter what either of them tries, the stock doesn't budge. So they keep parrying and thrusting. It's a sensational battle.

Once Icahn, the unpolished kid from Queens, has sunk his teeth into a company, he's nearly impossible to shake loose (unless, of course, said company's stock gets a lift, in which case he cashes out, and everyone's happy). "It took me four years," he reminds me, "but ultimately I made $4 billion with RJR."

News reports have said that Icahn's camp, which includes Lazard chief Bruce Wasserstein, is having trouble recruiting a board to rival Time Warner's (Research) in the coming proxy fight. Icahn denies it. "We will have no trouble putting up a slate with very credible individuals," he says. Icahn and his allies control 3.1 percent of the media giant's outstanding shares and don't appear to have the votes to prevail in the proxy battle.

But while Parsons and COO Jeff Bewkes must run their $42-billion-yearly-sales company while fending off this angry dog, Icahn can concentrate almost exclusively on barking and chasing Parsons' car.

An informed Wall Street source says Icahn has already rounded up some board candidates, including three former CEOs, a "respected" professor of corporate governance, and a former FCC commissioner. One source points to Reed Hundt, who served in the Clinton administration. Hundt, now an advisor to McKinsey, says he has "no intention of playing any role like that."

Icahn is also seeking to merge some of Time Warner's businesses -- AOL, the TV networks, and the movie studio -- with an Internet portal. A source says Icahn has had discussions with one or more portals about combining the businesses and then spinning off the publishing and cable operations.

And other sources confirm there have been discussions between Icahn's camp and IAC, the Internet company run by Barry Diller. How could Icahn pry those businesses out of Time Warner using IAC, given that TWX is nine times bigger than IAC (Research)? That's unclear. It's possible that Diller, Icahn, and Wasserstein could come up with additional partners. Right now Diller says the discussions are neither hot nor ongoing.

Icahn has also been interviewing candidates to replace Parsons as CEO. They might not be media types, but rather restructuring experts who'd cut what Icahn calls Time Warner's "bloated bureaucracy." Icahn points to his operation as a paradigm, saying that his funds now control companies with more than 30,000 employees and that he has no PR department and little overhead.

A Time Warner spokesman says it will respond when executives have a chance to read Lazard's voluminous proposal to make over Time Warner, which is expected to be released within weeks.

While Icahn doesn't appear to have anything close to a firm grip on Time Warner at the moment, counting him out would be a big mistake. Icahn is cunning, relentless, and extremely patient. Remember, he battled RJR for four years. He's only been in this fight for six months.

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ANDY SERWER, editor at large of FORTUNE, can be reached at aserwer@fortunemail.com. Read him online in Street Life on fortune.com and watch him on CNN's American Morning and In the Money.