Skype’s gone, so the next big thing for EBay is classifieds.

“I’m going to be very aggressive looking for opportunities to strengthen that portfolio, either organically or through acquisitions,” CEO John Donahoe told Bloomberg News in an interview published on Wednesday.

“We have the financial strength and capacity to do a sizeable acquisition. When we see an opportunity that will really strengthen the portfolio, we’ll move.”

EBay’s already big in classifieds, of course, with significant operations in more than 20 countries. It owns Mobile.de in Germany; Marktplaats.nl, a killer site in the Netherlands; Kijiji and its sister sites (Loquo, Gumtree and others), which are strong in Canada, the U.K., South Africa and other countries, and Rent.com, EBay Motors and others in the United States. Even so, when the CEO says he’s committing resources, that’s news.

(Here’s a current fact sheet about EBay classifieds, if you want more info.)

What might EBay buy?

Yahoo is purportedly trying to sell HotJobs. There’s a possibility. Another? Monster Worldwide. With a market capitalization under $2 billion, Monster and its global network of sites could be an acquisition target for EBay or any one of a dozen other media companies. In the U.S. there’s Move Inc., which is only valued at $250 million or so. (But two big questions about Move would be, “Will there ever be a profitable, sustainable business model here?” and “Would the National Association of Realtors allow EBay [or anyone] to retain the long-term exclusive deal that Move Inc. and Realtor.com have with the NAR?”) Globally, there are literally hundreds of sites and hybrid print / online classified businesses that would make a strong fit for EBay. Many could be grabbed at the right price.

Valuations of classified sites are deeply depressed right now because of economic issues. But for the long term, the best sites and classified publishing operations will prove to be extraordinarily lucrative businesses (especially the ones that don’t require a sizeable sales team). They can be expected to grow exponentially during the next few years. In Eastern Europe, Latin America, certain Asian markets and other regions, classifieds should far surpass typical Internet growth rates because of increases in adoption of online classifieds over print; growth in the use of interactive media, most notably mobile, and economic recovery.

It’s no secret that growth of EBay’s original core business has slowed, and Donahoe is looking around for sectors and businesses that could be a good fit with its traditional merchandise / auction model. EBay has already proven internally that classifieds can be lucrative, so now the question is, how to grow them.

“The Internet is dynamic enough that how buyers and sellers connect is going to continue to evolve,” Donahoe told Bloomberg reporter Joseph Galante. “We’re trying to build the biggest portfolio of formats and give the buyers and sellers choice.”

Lurking in the background of this aggressive new stance, of course, is the battle between Craigslist Inc. and its almost-25-percent owner EBay. The two have been at odds since EBay launched the competitive free-classified site Kijiji in the United States in 2007.

A trial starts Monday in Delaware Chancery Court in the EBay vs. Craigslist lawsuit; a separate lawsuit, filed by Craigslist against EBay in California, is pending. More about that here.