The Yahoo! Connected TV booth is shown during the 2011 International Consumer Electronics Show (CES) in Las Vegas
The Yahoo! Connected TV booth is shown during the 2011 International Consumer Electronics Show (CES) in Las Vegas, Nevada January 7, 2011. Yahoo! announced a new "broadcast interactivity" feature for the Yahoo! Connected TV platform and D-Link announced a Yahoo Connected TV media player that will support Yahoo's new interactive services on older televisions that are not Internet enabled. REUTERS

Could Facebook buy Yahoo, effectively killing two birds with one stone? That's a scenario suggested by Reuters financial blog Breakingviews, and it is not out of the question.

For one, Facebook is growing and growing, is private and because it allocates stock among its 2,000-plus employees, at some point will be forced by federal requirements to make public its financials. CEO Marc Zuckerberg has made no secret that Facebook would like to go public.

Now look at Yahoo, which just ousted CEO Carol Bartz, attracted an activist shareholder who bought a 5.1 percent stake and hired Allen & Co., an investment bank, for financial advice that could include spinoffs and even a possible sale.

Yahoo is not cheap. Based on Monday's closing price of $14.26, it has a market capitalization of $18 billion and enterprise value of $15.49 billion, the figure Allen looks at, as well as a potential buyer.

If a thriving but private Facebook were to bid for a Yahoo that's in flux, the result could be a thriving site. Facebook would have Yahoo's search and news sites, entertainment and a unified advertising platform. Additionally, Facebook employee shares would be used to buy Yahoo shares, so this reverse takeover could constitute a kind of backdoor IPO. Facebook employees would have Yahoo shares; the whole enterprise could be renamed Facebook.

This tactic might not be a sexy or attractive, or even get Zuckerberg on CNBC the day he rang the bell at one of the stock exchanges. But it might be an interesting marriage.

Yahoo, based in Sunnyvale, Calif., has a board of mainly second-tier executives, from accounting and advertising, as well as Akamai president David Kenny.

Facebook, in nearby Palo Alto, Calif., has a higher-profile board. This week, it added former White House Chief of Staff Erskine Bowles to a group that includes Marc Andreesen, the Netscape founder; Reed Hastings, CEO of Netflix; Donald Graham, CEO of Washington Post, as well as crackerjack venture capitalist Jim Breyer of Accel Partners.

Boards like these can do the math and figure out how to do it, particularly in a time when the stock markets are sour. They could also get some help from Microsoft, whose Bing search engine handles mechanical functions for Yahoo and also owns a piece of Facebook. Microsoft had $52.7 billion in cash in June, some required to buy Skype.

Besides Zuckerberg, Facebook, with as many as 750 million users, has a respected COO, Sheryl Sandberg, former VP of global online sales and operations for Google.

The scenario is a little thorny, but doable. It could be an interesting one for both Facebook and Yahoo.