Yahoo Inc.’s inability to snap out of a financial funk may be about to turn the embattled Internet company into a takeover target for the second time in less than three years.

That possibility, floated in a story posted online late Wednesday by The Wall Street Journal, lifted Yahoo’s shares by nearly 13 percent in Wednesday’s after-hours trading.

After snubbing a $47.5 billion buyout offer from the much larger Microsoft Corp. in 2008, Yahoo (Nasdaq: YHOO) this time may find itself being courted by a smaller rival with its own problems, AOL Inc.

If Yahoo gets another offer, it will likely be for considerably less than what the company could have gotten had it embraced Microsoft. Yahoo’s market value now is less than $25 billion, even after factoring in the runup from the takeover speculation.

Still, it appears AOL realizes it would need to bring in more financial muscle to get a deal done. The company, based in New York, is discussing the possible Yahoo offer with several firms that specialize in buying companies whose stocks have fallen out of favor, according to the Journal.

The story identified Silver Lake Partners and Blackstone Group LP as two of the firms huddling with AOL. The Journal cited unnamed people familiar with the talks, which were described as preliminary.

Yahoo hadn’t been contacted by AOL or any of the other potential suitors, the Journal said.

Both AOL and Yahoo declined to comment. Silver Lake and Blackstone didn’t immediately return phone calls.

Yahoo has been testing the patience of its shareholders for the past four years, as its financial performance flagged while the once-smaller Google Inc. blossomed into the Internet’s most profitable company. More recently, Yahoo has been upstaged by rapidly growing Web hangouts such as Facebook and Twitter.

Three different CEOs have tried to turn around Yahoo with little success. After former movie studio boss Terry Semel resigned under shareholder pressure in mid-2007, Yahoo co-founder Jerry Yang took over the helm and wound up spending much of his reign trying to fend off Microsoft’s advances.

While trying to thwart Microsoft, Yang discussed possible deals with AOL while it was still part of Time Warner Inc. and with News Corp., which owns in addition to The Wall Street Journal and the Fox television network.

Microsoft finally withdrew its last offer of $33 per share in May 2008. Yahoo shares gained $1.97 in extended trading after finishing the regular session at $15.25, up 82 cents.

Yahoo, which is based in Sunnyvale, promised better times when it brought in tough-talking Silicon Valley veteran Carol Bartz as CEO in January 2009, but she hasn’t been able to spur revenue growth so far.

Bartz has shaken things up by cutting costs, shutting down unprofitable services and negotiating an Internet search partnership with Microsoft.

But some of her ideas and blunt comments seem to have alienated Yahoo’s work force. The internal unrest has became more visible as other Yahoo top executives defect from the company.

Some of Bartz’s comments also may have ruffled some feathers at Alibaba Group, a Chinese Internet company in which Yahoo owns a 39 percent stake. If that’s true, Alibaba CEO Jack Ma conceivably could help potential Yahoo bidders to finance a takeover by agreeing to buy back Yahoo’s stake in his company after a deal is done.

And if Yahoo shareholders or the company’s board are tired of Bartz’s leadership, selling to AOL would be one way of bringing in fresh face who is highly regarded in technology and media circles.

AOL is run by Tim Armstrong, a former Google executive who is trying to feature more unique content on AOL in an effort to bring in more advertising revenue.

Those efforts haven’t done much yet. AOL’s revenue fell 25 percent to $1.24 billion during the first half of this year. Yahoo’s revenue increased 1 percent

If it were to buy Yahoo, AOL would gain access to one of the Internet’s largest audiences as it tries to burnish its own brand.

The specter of a possible takeover bid will likely intensify the interest in Yahoo’s third-quarter earnings report due out next Tuesday. Analysts are already bracing for another round of lackluster results, and if that holds true, it could set the stage for an offer.

Microsoft launched its unsolicited takeover bid in early 2008, just days after Yahoo announced a disappointing quarterly performance.

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