Trading activity on's (Nasdaq: SOHU) options was on fire yesterday, as speculators bought into a rumor that Baidu (Nasdaq: BIDU) would be making a play for its new media rival.

The rumor appears to be baseless, though it does make sense on a few different levels.

For starters, nearly any company that Baidu would purchase would be accretive to earnings, given its heady valuation. Baidu is trading at 60 times this year's projected profitability, and 39 times next year's bottom-line target.

Sohu, on the other hand, fetches more reasonable earnings multiples of 15 and 12 in 2010 and 2011, respectively. Aside from leading travel portal (Nasdaq: CTRP) at 34 times next year's earnings target -- and SINA (Nasdaq: SINA) at 22 -- most of China's publicly traded dot-coms fetch forward profit multiples in the teens or lower.

There's a catch, of course. Baidu's growth is also worth the premium. Its latest quarter found China's leading search engine growing revenue by 74%, with net income more than doubling. Sohu's top line only mustered a 15% year-over-year advance during the same quarter, and earnings barely climbed at all.

So why are market whisperers playing matchmaker? Well, Sohu runs Sogou -- a small search engine. Baidu doesn't need Sogou to pad its market dominance, but it certainly wouldn't hurt.

Sohu also is a serious player in online gaming, given its majority stake in (Nasdaq: CYOU). This normally wouldn't seem to be a good fit for Baidu, but keep in mind that it recently began hosting third-party apps on its website. Adding a leading developer of multiplayer fantasy games to its arsenal could come in handy.

Any such deal remains unlikely to happen, though. Baidu has the financial means to pull off an acquisition of $2 billion or more, but it really hasn't gone that route in the past. If Baidu wanted to grow through buyouts, it could have easily picked up the majority stake in Focus Media's (Nasdaq: FMCN) Allyes online advertising subsidiary, which was sold off this summer.  

Baidu's just not a buyer. I'm guessing that whoever started this rumor sold off their speculative stake in Sohu during yesterday's run-up.

What should Baidu buy, if it really is on the acquisition path? Share your thoughts in the comment box below.

Baidu and are Motley Fool Rule Breakers selections. Sina is a Motley Fool Stock Advisor pick. International is a Motley Fool Hidden Gems recommendation. Try any of our Foolish newsletter services free for 30 days. True to its name, The Motley Fool is made up of a motley assortment of writers and analysts, each with a unique perspective; sometimes we agree, sometimes we disagree, but we all believe in the power of learning from each other through our Foolish community.

Longtime Fool contributor Rick Munarriz has been a fan of China’s high-margin online stocks for a long time. He does not own shares in any of the companies in this story. He is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early. The Fool has a disclosure policy.