The long-beleaguered search engine company Yahoo! Inc. would probably be better off selling off pieces of itself rather than submit to a takeover in whole, given that the separate segments of the firm probably have more value than the sum of the individual parts.

Yahoo is reportedly fielding offers from multiple parties and has hired the boutique investment bank Allen & Co. to evaluate such proposals in order to maximize shareholder value.

However, any such potential transaction won’t happen overnight.

According to a leaked memo that Yahoo executive Jerry Yang sent to employees, he said: “We will take the time we need to select and structure the best approach for the company, its shareholders and employees. While we will move with a sense of urgency, this process will take time. Months, not weeks.

Robert Phillips, managing principal at Spectrum Management in Indianapolis, said that Yahoo’s most attractive assets are its stakes in the fast-growing Yahoo Japan (35-percent owned by Yahoo), the dominant search company in Japan; and China-based internet firm Alibaba Group (43 percent-owned by Yahoo).

However, although its U.S. business is relatively flat, Yahoo still remains the second most popular search engine (behind the behemoth that is Google) with about 16 percent of the market; and also delivers solidly growing display advertising revenues.

Indeed, the company’s display revenue climbed by 5 percent in the second quarter (although much of that growth came from overseas).

The main problem is satisfying Yahoo stockholders who are fatigued by a share price that has been going nowhere for well over a decade.

“Ever since [former CEO] Jerry Yang turned down Microsoft Corp.’s $33-per-share takeover bid in 2008, Yahoo stockholders have been clamoring for more increased value,” Phillips said. “That $33-figure is hanging over the company’s head.”

The Microsoft deal valued Yahoo at $47.5-billion (versus its current valuation of about $18.6-billion).

Phillips estimates that by selling off appealing pieces like Alibaba and Yahoo Japan, and perhaps a few others, Yahoo could increase the overall company’s valuation significantly above the current $15 price, though probably not close to the $33 price Microsoft once offered.

An investment group led by Silver Lake Partners, a private equity firm that specializes in the technology space, recently made an additional $1.6-billion investment in Alibaba, sparking rumors that Silver Lake might make a bid for Yahoo itself.

The latest Alibaba investment values the company at about $32-billion (which is larger than Yahoo’s entire market cap).

Another private equity firm, Providence Equity Partners, has also been rumored to make a bid for parts or all of Yahoo.

Meanwhile, should Yahoo actually be on the market, it needs to revive growth and make it ever more attractive to potential suitors. The recent firing of chief executive Carol Bartz probably marked the first salvo in the company’s plan to overhaul itself.

Phillips pointed out that while Bartz was able to cut some costs early in her reign, she was unable to articulate any kind of strategic vision or direction for the company that would appease long-suffering shareholders. Indeed, not only did Yahoo lose search engine business to Google, but it also completely missed out social and mobile media.

Phillips also suggests that the delay in finding a permanent replacement for Bartz might also signal that a break-up is in the works.

Meanwhile, major shareholders are pushing for big changes. Recently, Third Point LLC, which is owned by hedge fund manager Daniel Loeb, bought a 5.2 percent stake in Yahoo and demanded that the company’s board resign.

Interestingly, Yahoo shares have been climbing steadily – up about 12.7 percent since early August (long before Bartz’s firing), suggesting perhaps that investors are anticipating a takeover or break-up.