Today's headscratcher is a report from Business Insider that AOL has started a process that could result in its sale to Microsoft. Despite the reasons cited in the report -- including Microsoft's desperation to gain ground against Google -- the speculation doesn't make much sense.

That didn't stop the rumor from sparking a rally in AOL's shares, at one point pushing them up more than 5 percent before cooler heads apparently prevailed and the stock settled in at a more modest but still puzzling 1.3 percent gain on a day when the broader NASDAQ slid.

The rumor has its origins in AOL CEO Tim Armstrong's comment this week at the D8 conference that the company is considering the possibility of working with a new search partner after 10 years with Google. With Microsoft taking over Yahoo's search business, that makes the Redmond company about the only other viable candidate for the job. So it wouldn't be a surprise to see the companies work out a search deal.

But a full-blown acquisition of AOL by Microsoft? That's what Business Insider says, quoting a "source familiar with Tim and AOL's strategic thinking" who suggests that "an outcome of these negotiations could be AOL's sale to Microsoft." It adds, "And even if this informed speculation proves false, it's a fact that whoever does sign AOL to a long term search deal will have the inside track to an eventual acquisition."

Even with that hedge, the whole thing seems a stretch.

At a market value of $2.27 billion, AOL wouldn't be a huge stretch for Microsoft financially. The Redmond company had nearly $40 billion in cash and equivalents at the end of March. But the problem with the theory is that Microsoft has been focusing heavily on its search business, to the detriment of its other online businesses, as evidenced in part by the aftermath of the company's $6 billion aQuantive acquisition.

Peter Klein, Microsoft's chief financial officer, said recently that the company is unlikely to attempt any "mega-acquisitions" in the near future, and AOL would certainly qualify. The time for Microsoft to

And there's a lot more to AOL than search, including a sizeable advertising business, web content and Internet access. Sure, elements of AOL could fit into MSN, but not enough to justify a big deal. With Microsoft focused heavily on incorporating Yahoo's search operations into its own, it would be a huge surprise to see the company go out on a limb to pursue a full-blown AOL acquisition,

"Seems very unlikely," said Matt Rosoff, an analyst at the Kirkland-based Directions on Microsoft research firm. "I’ve seen and heard these rumors on and off for years. It seems like it would be overkill if they’re just trying to get a search deal."

AOL's search market share in the U.S. was 2.4 percent in April, according to comScore Networks, compared with 11.8 percent for Microsoft, 17.7 percent for Yahoo and 64.4 percent for Google.