It looks like shares of Palm, Inc. (PALM) are going to continue rising as long as there’s a potential buyer out there, regardless of how remote the chance that a buyer may actually pull the trigger on a deal. Palm’s most recent potential buyer, Taiwan smartphone maker HTC Corp., has decided to take a pass on the purchase according to sources cited in a Reuters story. “There just weren’t enough synergies to take the deal forward,” the source is reported to have said.

In other words, even if it fired every Palm employee, HTC still gets nothing from acquiring Palm. The analyst at Canaccord Adams who said a few weeks ago that Palm is worth zero might have been on to something.

Palm CEO Jon Rubinstein is reportedly seeking a buyer with $1.3 billion in cash to spend. That’s about a 50% premium above the company’s market cap today, and there is virtually no chance Palm shareholders will realize that price. Far likelier is a price very near the $850 million or so market cap. And even that would be a gift because the company’s book value/share is negative, -$1.77/share.

The latest rumored white knight is China’s Lenovo Group. But Lenovo, which bought the PC hardware business of IBM Corp. (IBM) in 2005 for about $1.75 billion in cash is not likely to pay Palm’s asking price. At the time of the PC deal, IBM was getting about $11 billion annually in revenue from its PC business, but the US computer giant was realizing no profit on the hardware and was getting rid of all its hardware businesses anyway as it shifted to services company. Lenovo got a bargain then, but Palm is in no way similar.

Lenovo is prepping to launch a smartphone into the Chinese market next month, the LePhone, which uses Google’s (GOOG) Android operating system. Lenovo expects to sell millions of the LePhones in China in the next five years, with sales growing into the tens of millions after that. Palm adds nothing to that scenario except confusion.

One positive feature of Palm is its brand recognition in the US, where a LePhone launch has not yet been announced. But why would Lenovo want to try to market a product that is both incompatible with its own LePhone and already losing share in the US market? The company would have to be smoking some pretty fun cigarettes to want to do this.

PC makers such as Acer, Asustek, and Dell Inc. (DELL) already have phones either on the market or on their way. And if there’s a buyer at all for Palm, it would seem that it would be a PC maker wanting an easy way into the mobile smartphone market. Only Hewlett-Packard (HPQ) remains a likely suspect.

H-P has the cash to buy Palm and has so far been unable to crack the smartphone market with its own phones. The company’s efforts have been half-hearted at best, and adding the Palm webOS operating system and Palm hardware to its product offerings would mean that it would have to drop the Windows Mobile OS it has been selling or support two operating systems. Once again, the synergies don’t appear to be there.

Palm’s options are running out, but investors keep seeing that white knight just around the corner. The company’s shares are up about 4% today for no apparent reason other than perhaps because the company hasn’t yet filed for bankruptcy protection.

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