Rumors that Time Warner's (NYSE:TWX) languishing America Online service is on the bidding block have been around for some time. Whether it was last year's report that Microsoft (NASDAQ:MSFT) was snooping around or whispers that former chieftain Steve Case was looking to take back the company he navigated toward prominence, the speculation -- which invariably stemmed from third-party sources -- was ultimately unfounded.

But yesterday, at the D3: All Things Digital conference in California, InterActive Corp (NASDAQ:IACI) CEO Barry Diller mentioned that his company was once looking to buy AOL, but scoffed at the $20 billion asking price.

Wait a minute. That's no third party talking. That's a real name with a real price, presumably proposed by Time Warner. While we don't know how it all went down -- or if AOL is still up for sale -- it is an intriguing tidbit. With $20.5 billion in debt, the alleged asking price would help the company wipe its leveraged balance sheet clean.

Then again, selling AOL could also prove to be a huge mistake for Time Warner. Sure, AOL's domestic subscriber base has shrunk from 26.7 million members to 21.7 million over the past two-and-a-half years. That's not the point. Thanks to the vibrant online advertising market, AOL posted a 17% spike in operating profits this past quarter despite the gradual subscriber defections.

AOL is also a potent platform to help market Time Warner's plethora of entertainment products. With cheaper online connectivity available from other providers like United Online (NASDAQ:UNTD), one would assume that the AOL crowd is a more lucrative target audience with more disposable income to spend.

That's why the bigger question isn't whether AOL is for sale, but why Time Warner would want to sell it in the first place. Don't do it, Time Warner. It would be like selling your hair to buy a hairbrush.

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Longtime Fool contributor Rick Munarriz has been an AOL subscriber since 1992 but he doesn't own any of the stocks mentioned in this story. The Fool has a disclosure policy. Rick is also part of the Rule Breakers newsletter research team, seeking out tomorrow's ultimate growth stocks a day early.