Yahoo! Inc. should call Microsoft Corp.’s bluff. That may sound odd given the software giant’s apparent disdain for its former sweetheart. But everyone continues to lose ground to Google Inc. in search.

Yahoo denied a report in the Sunday Times that Microsoft was backing a group planning to acquire the Internet company’s search business and install new management led by former AOL Llc. chief Jonathan Miller and former Fox Interactive Media Inc. boss Ross Levinsohn.

Yahoo says it could stop the slide in market share if it just had scale. It should put its money where its mouth is and offer to buy Microsoft’s MSN unit with a public bear-hug.

Yahoo has little to lose. Its stock is trading two-thirds below Microsoft’s $31 (Rs1,553 today) February bid. Its proposed partnership with Google was dropped by the search group a few weeks ago, and Microsoft chief Steve Ballmer continues to publicly spurn reconciliation attempts. This pile of disappointment led to Jerry Yang’s recent resignation.

Meanwhile, Google keeps hoovering up market share in the search business—at everyone else’s expense. The latest figures show it has a dominant 63% share of the US market, an 8% increase over the last year, according to digital market research firm Comscore Inc. Yahoo has been one of the biggest losers. Its share now resides at a measly 20%.

Yahoo executives say they can reverse this with greater scale. Search does snowball, they say, so incremental gains matter. The more searches a service attracts, the more effective its search algorithm becomes. These better search results bring even more activity, creating a virtuous cycle.

If Yahoo really believes this argument, it should offer to buy Microsoft’s MSN division. The online and search unit is equally challenged by Google and has just 8.5% of the US search market. Moreover, many Microsoft shareholders would love to see the company jettison a business that has been a constant management distraction and a money loser.

What’s it worth? As a guide, one could use Google’s market cap, which assigns about $1.5 billion of value for each percentage point of market share. Discount that by a third to reflect Google’s dominance, and MSN might be worth some $8 billion. With Yahoo worth twice that much, it could offer to take MSN off Microsoft’s hands for stock, giving Microsoft a third of the resulting combination and exposure to any value the deal creates.

There’s another benefit to Yahoo of going on the offensive. By forcing Microsoft to defend its sub-scale search position, Yahoo might get its rival to admit that its bigger worry is the threat of so-called cloud computing to its core software business.

Ballmer has been able to crater Yahoo’s stock simply by opening his mouth. A public bid could give similar power to Yahoo.

And there’s always the chance that in its own defence, the bigger bear might just find it more convenient to squelch a smaller, peskier cub by gobbling it up.