Bloomberg News reported earlier in the week that eBay (EBAY) finance chief Bob Swan was asked at a CSFB technology conference whether eBay would sell Skype, the computer phone calling service it bought three years ago for far too much money. The question followed the slimmest of rumors on a British newspaper’s Web site: “Currently in favour around London’s webbist community is the rumour that Google (GOOG) has been in negotiations to buy Skype,” wrote Guardian blogger Jemima Kiss. (Great name!)

According to my own reporting in the “webbist community” in Silicon Valley, Swan discussed the wrong prospective asset sale. He should have addressed whether eBay would sell PayPal. It’s no secret that PayPal is blazing, and it’s so-called off eBay business, the payments it processes for non-eBay transactions, is becoming an ever-larger part of PayPal’s overall business. (For a detailed and highly readable overview of eBay’s business, including a comparison of its “marketplaces” and “payments” units, see Swan’s own pre-Q&A presentation at the CSFB conference.)

Two different Silicon Valley investors, in separate conversations this week, pointed out to me the embarrassment that Amazon (AMZN), with its market capitalization of $37 billion, had caught up to — and effectively surpassed — eBay (market cap: $45 billion), if you take out the value of PayPal. Ebay is a natural monopoly, the far-and-away leader in online auctions and carries no inventory. Amazon is a retailer with slim margins and a not easily defended business. The easiest way for eBay to reward its investors, they argued, would be to spin off PayPal, a move eBay management will never acknowledge considering — until the day a plan is announced. (A tip of the hat, by the way, for the second day in a row to the insightful Web site breakingviews.com, which examined the eBay breakup scenario on Nov. 7.)

Surely there are companies out there that could make better use of Skype than eBay has. But selling it won’t give eBay’s stock the pop it needs. Setting free PayPal might.

I sat down Tuesday afternoon in Mountain View, Calif., with Dan Nye, the newish CEO (he joined earlier this year) of LinkedIn. That’s the company that is like Facebook for grownups, a businessperson’s social networking site. Nye’s looking for press because LinkedIn plans to unveil some nifty new features on Dec. 10. (I got a look, but agreed not to divulge anything yet.) I was interested in hearing what he had to say, in part because of the rumors flying around that LinkedIn plans to sell the company early next year to News Corp. (NWS)

The buyout gossip began with an item last week in the UK version of TechCrunch. Never mind that LinkedIn founder Reid Hoffman (a made man in the PayPal mafia and a buddy of mine) categorically denied the rumor in the Daily Telegraph. Anything that suggests that Rupert Murdoch would expand his social-networking empire is sure to set tongues wagging. Breakingviews.com wrote an intelligent summary of why a LinkedIn acquisition would make sense, largely because of the opportunities to leverage LinkedIn’s tools with the Wall Street Journal readership.

Not surprisingly, Nye didn’t deny that News Corp. made an offer for his company. Instead, he said that when he joined the company he told the board — comprised of Hoffman, Sequoia’s Mark Kvamme and Greylock’s David Sze — that he was only interested in taking the job if the goal was to “go long.” But is he selling out anyway? “We’re excited about building this company,” said Nye. “It would take a helluva lot to get us off that path.” Does that mean $1 billion? “A lot more than that,” said Nye, who worked at Procter & Gamble (PG), Intuit (INTU) and Advent Software (ADVS) before joining LinkedIn.

LinkedIn clearly is playing to win. The company has mushroomed from 60 employees when Nye joined in February to almost 200 today. At the time, LinkedIn had 9 million members; today it has nearly 17 million. Nye predicted revenues will range from $75 million to $100 million next year.

LinkedIn has the virtue of having survived adversity. Before Facebook and MySpace existed — back when Friendster was hot — LinkedIn was just getting going. It’s still going. Independent or part of News Corp., it’s fun watching this plucky company succeed.