(FORTUNE Magazine) - Leading headhunters agree: The No. 1 draft pick in the game of grabbing top executive talent -- the most lusted-after managerial star who isn't already a CEO -- is David Calhoun of General Electric.

"He's the top of the list," says Gerry Roche of executive search firm Heidrick & Struggles. "He's the complete package," says Roche's archrival, Tom Neff of SpencerStuart. In this game, if Roche and Neff say you're it, you're it.

David Calhoun, General Electric

More from Fortune Behind the dollar's tear Lehman collapse socks hedge fund Lime Wire seeks legitimacy FORTUNE 500 Current Issue Subscribe to Fortune

The thing about top draft choices is that they're hard to sign. Calhoun was on the very short list to be Boeing's new CEO last year. Soon after the job went to a former GE star, 3M chief James McNerney, Calhoun was promoted to the post of vice chairman at GE (Research). It appears that GE boss Jeff Immelt did what it took to keep Calhoun on board, though everyone involved is officially tight-lipped.

Calhoun just says, "My heart and soul are in GE. This opportunity is very appealing to me."

So why won't the headhunters leave Calhoun alone? One measure of his appeal is a hugely impressive, carefully crafted GE resume. He came to the company in 1979 right out of Virginia Tech (major: accounting) and immediately stood out. Rapid promotions took him through the company's wide range of businesses.

That's one reason GE executives are so esteemed: Virtually no other company can give managers such varied experiences.

And because GE is unsurpassed at leadership development, those experiences are chosen very deliberately. It's no accident that Calhoun has run two long-cycle businesses (railroad locomotives and jet engines), one short-cycle business (lighting), and a financial services business (reinsurance), or that one of those was a consumer business (lighting) and one a defense business (jet engines), or that he has had a major overseas posting (running GE Plastics in Asia).

He's the complete package.

What the resume can't convey are personal traits that recruiters also salivate over. He seems, dare one say it, as energetic as former CEO Jack Welch. Ask him for his idea of fun, and he says: work.

"When I wake up in the morning, this is what I enjoy doing. I love it." He also loves sports -- skiing, golf, tennis, pickup basketball -- reflecting an intense competitiveness that is, he says, his "framework" for everything. His passion is infectious -- as a speaker, he can get his audience wound up and ready to run through walls-- and he's comfortable in his own skin: a cement salesman's son, an aggressive, high-IQ guy from eastern Pennsylvania with a powerful desire to win.

As Welch says, "You've got to be comfortable with yourself to make a good boss."

The big question about Dave Calhoun is how badly he wants to be the boss. It's easy to believe him when he says he likes his current gig. He's overseeing businesses with some $40 billion of sales. If they were free-standing instead of inside GE, he'd already be one of America's most prominent CEOs.

Whether he pines to run his own show is a question he very prudently won't answer. But we know a couple of things.

First, the one company he won't run is GE, since he's 48 and Immelt is 49.

And second, offers of the world's best CEO jobs will continue coming over the transom. It's hard to imagine how anyone could keep saying no forever.