Go Daddy GirlGo Daddy has built a name for itself as the place to buy domain names with its risqué Super Bowl ads. But could it land in Jeff Bezos’s shopping cart?

The Scottsdale, Ariz.-based domain-name registrar has put itself up for sale, reports the Wall Street Journal, at a price that could top $1 billion. Qatalyst Partners, run by Frank Quattrone, the famous Silicon Valley investment banker, is handling the auction.

Private-equity firms, which have purchased other domain-name companies for their reliable cash flows, are obvious bidders. But a tech observer has a different buyer in mind: Amazon.com.

At first, it seems like an odd fit. Go Daddy, with 43 million registered domains, is one of the largest domain-name companies. It’s currently privately owned by Bob Parsons, an eccentric entrepreneur known for his taste for big trucks and ribald language. Ascetic Amazon founder Jeff Bezos doesn’t exactly seem like a kindred spirit, although he has on occasion made remarks about his sex life.

Jesse Ma, a lawyer at New York-based Gawker Media, the publisher of several influential tech and celebrity websites, suggests on his personal blog that Amazon.com should buy Go Daddy to bolster its Web-services arm, which rents out computing power and storage to startups and other customers.

Amazon has also dabbled in selling keyword advertising through its Clickriver service, which could in theory power Go Daddy’s parked domains, which have been registered but not yet filled with content.

It is, in short, a sexy notion.

Here’s one more connection: Quattrone was the banker who took Amazon public in the mid-’90s.