(FORTUNE Magazine) – It's the highest-profile corporate beauty pageant of 2004--but does any star executive want the tiara? That's the burning question at Coca-Cola now as the powerful board of directors at the beleaguered drink giant struggles to hire a new CEO by summer. Home Depot CEO Bob Nardelli, who is a Coke director, and 3M CEO Jim McNerney both spurned overtures from the board early on.

Turns out that running Coke isn't the plum gig it once was. Bad news just keeps bubbling out of the company: The April disclosure that general counsel Deval Patrick, who was charged with responding to federal probes into Coke's accounting, will retire is just the latest worrisome incident. While Coke's laggard business in key markets like North America and Japan is strengthening, a serious brain drain handicaps Coke's recovery, and outgoing CEO Doug Daft is in charge only by title. Meanwhile, corporate governance critics oppose the reelection of several directors, including Warren Buffett and Herbert Allen.

Now, of the five outside candidates under consideration, a front-runner has emerged: Gillette CEO Jim Kilts. But it may take big-time wooing to persuade him to accept the job. Not that Kilts shies from corporate messes. He headed Kraft and Nabisco, and Gillette's board lured him away in early 2001 after assuring him that major problems existed and only a disciplined pro could turn the company around. Kilts did it: He wrestled down costs, strengthened the balance sheet, and improved profits. When several Coke directors floated his name, some worried that Kilts, a sober boss, lacked enough passion to lead Coke. The fact that he is a favorite of Buffett's, a large shareholder in Gillette as well as Coke, has swayed some doubters (governance critics notwithstanding, Buffett's opinion holds a tremendous amount of weight). One sticking point is that neither Kilts, 56, nor his wife, Sandy, want to move from Rye, N.Y., the Westchester suburb where they have lived for many years. Kilts recently renewed his Gillette contract through January 2006, and his current job suits his lifestyle: He commutes to Boston headquarters weekly on Amtrak's high-speed Acela train. Commuting from Rye isn't an option at Coke--and not just because Kilts is a white-knuckle flier. He's been told that he must move to Atlanta.

If Kilts doesn't work out, Coke will probably choose from four other candidates: Mattel CEO Bob Eckert, who was Kilts's protege at Kraft, has the squeaky-clean image the company needs, but he lacks Kilts's stature and deep international experience. Kellogg CEO Carlos Gutierrez has staged a turnaround at that company, but it's not in the same league as Coca-Cola. Kerry Clark, one of two vice chairmen under A.G. Lafley at Procter & Gamble, has the disadvantage of never having run a publicly held company. Coke's directors are considering one outsider who used to be an insider: Neville Isdell, who in 1997 lost the CEO race to the Doug before Daft, Doug Ivester. A tall, charismatic Irishman who led Coke's European business in the '90s, Isdell, 61, quit to head one of its publicly owned bottlers, Coca-Cola Beverages, and retired three years ago to live in Barbados. "He's hands-on, detail-oriented, and engaged, and has all the skill sets to run Coke," says CSFB analyst Andrew Conway. "The only negative is that he's been on the beach for a period." Don Keough, Coke's former president who is heading the CEO search, is known to be a big fan of Isdell's.

A prevailing concern is that Coke needs fresh blood--which is bad news for the man who lusts for the job: Coke president Steve Heyer. Viewed as a terrific operator but too brash to be CEO, Heyer has all but slipped out of the running for the top post. If he bolts when a new chief comes in, the new boss will have to clean up the mess and fill the seat beside him.

--Patricia Sellers