What if Microsoft bought Yahoo? According to a report from Reuters, Microsoft is eyeing a bid on the company which is currently down a CEO.

Would such an acquisition be good for Microsoft? Good for Yahoo? Tell us what you think.

Yahoo’s board fired CEO Carol Bartz last month, and has yet to find a replacement beyond interim CEO Timothy Morse. According to at least one report, former CEO Jerry Yang had even assumed control at the company (though this is unconfirmed). The company source cited in that report from Business Insider said it was “f-ing crazy”.

The Reuters report cites “sources close to the situation,” and says, “Microsoft joins a host of other companies looking at Yahoo, which has a market value of about $20 billion and is readying financial pitch books for potential buyers, they said.”

The other companies reportedly include Providence Equity Partners, Hellman & Friedman and Silver Lake Partners, Alibaba, and DST Global.

“Microsoft could easily afford Yahoo. After a 10% stock price bump on a report that Microsoft was weighing a bid, Yahoo’s market capitalization was about $21 billion,” says the Wall Street Journal. “If Microsoft offered $20 a share, 25% above Wednesday’s close, the price would be about $26 billion. But the net cost could be less than half that, assuming Microsoft sold Yahoo’s Asian assets and factoring in its $2.6 billion of cash.”

If you’ll recall, Microsoft made a failed attempt to take over Yahoo a few years ago, but ultimately ended up forming a “search alliance,” where the two companies would partner on search and advertising. Bing has been powering Yahoo’s search results since that went into effect. Microsoft’s bid for the company in 2008 was a reported $44.6 billion.

Given the amount of attention we (and our readers) place on search, it’s easy to get caught up in Yahoo the search engine, but Yahoo has a lot of properties, and some of them are quite powerful. A few months ago, the company shared this infographic as a reminder:

In its last earnings report, Yahoo said it is home to nine #1 properties globally, and is in the top three in 23 categories. It also said it has nine out of the top ten original video programs on the web.

Yahoo considers itself a media company, and that certainly is an area where Microsoft could grow. It would be interesting to see how the regulatory process plays out if this goes forward.

Regarding Yahoo and search, the company recently put up a blog post talking about how it’s ready for a “search fight,” including these three bullet points on “what search looks like” to Yahoo over the next 18 months:

• From destination to companion: Access and convenience are two key components in the search game. In the next 18 months, Search will be a companion experience that gives you answers immediately and instantly without leaving the page you are on – effortlessly.

• From fragmented to seamless: Consistency and simplicity are two key components in the search game. Users are increasingly searching on multiple devices. In the next 18 months, your devices and platforms will be seamlessly connected, allowing you to start an experience on one device and continue effortlessly onto another, with simple access to any information on any other devices. Search will be evolving into a beautiful and consistent multi-modal experience that simply integrates into your everyday life.

• From more information to better information: Relevancy and depth are two key components in the search game. When you search for something — say, Adirondack chairs — do you really care that we returned 9,150,000 results? Probably not. In the next 18 months, Search will focus on a deep experience that gives you only what you want to know, taking into account your search history, click behavior, demographics, social graph, and browsing history to provide you with a 1:1 experience. It will tell you why it served you the results it did and allow you to pivot on a number of aspects to further tune the page. It will no longer be a search engine designed for the masses, it will be a search engine tailored just for you. Some call it a results page; I call it an intent satisfaction experience.

Last month, Yahoo redesigned its search results pages.

Bing and Yahoo were both up in the U.S. search market reports last month, with Bing-powered search accounting for 28.99% of the market, according to Experian Hitwise.

Do you think Microsoft should buy Yahoo? Let us know in the comments.