When nature wanted to express its sense of humor, it created the platypus: a creature composed of the features of so many other mammals that when naturalists first stumbled on it they thought it was an elaborate hoax.

If fashion were to have an equivalent, it could be a mash up of Coach (COH) and London's Burberry: an elaborate construct of luxury goods that would -- on the face of it, at least -- seem like a match, but that, more likely would prove to be what one analysts dismissing the suggestion described as "a merger of problems."

Nevertheless, rumors of a combination of the two luxury goods purveyors have skated around the fashion blogs the last two weeks, and don't seem to be going away anytime soon.

The British investment site Betaville reported late last month that Coach has hired Evercore Partners (EVR) to facilitate what it said could be a $20 billion merger. Further accounts on the British blog seemed willing to entertain the possibility that the report could be farfetched.

But the talk does seem to have some legs, even if most of those accounts slip into either the "yes, with a but ...." Or "no, with a maybe ...." sort of explanations. Shares of Burberry, which popped in London late last month on the report, remain at what seem like elevated levels. Earlier this week, Coach reported fiscal first-quarter results that showed that sales inched up over last year's total, but nevertheless fell a little short of analysts' forecasts. The stock wasn't made to suffer, however, as shares added 3%, expanding the gains the stock has notched this year.

"My first thought was that this (report of a merger) is one of those that isn't blatantly obvious," Kathy Gersch, executive vice president of leadership consulting firm Kotter International, said in a recent interview. She added, "It's also not so far outside the realm of possibility."

Gersch acknowledged, "There are benefits, but lots of challenges" to any combination of the two legacy luxury brands.

One of the attractions of either brands is, as a Morningstar analysis following Coach's earnings release pointed out, the value of the company's cash flow potential, which could make it--rather than Burberry--the attractive buyout candidate. Financial sponsors have been rumored to be sniffing around the company, though none have identified themselves as a prospective buyer.

Morningstar, responding to the first quarter results at Coach, described the company's positive top-line growth and margin expansion as "an even more notable achievement when taking into account handbag and retail traffic headwinds."

Those headwinds prompted Coach earlier this year to move to remove sales of its handbags and other accessories from a quarter of its department store retail partners. The initiative was undertaken to alleviate some of the heavy promotional activity that department stores undertake to boost store traffic and enhance sales. However, luxury goods makers, including Coach, feel that discounting their products in these channels damages the brand. Management has talked extensively of elevating the brand.

However, the promotional activity at department store retailers has the effect of cheapening the product, which seems to turn off younger shoppers who are aspirational in nature. At worst that could leave the discounted luxury products brands to seem like something their - gasp - mothers would buy.

That underscores one of the prospective stumbling blocks between a Coach-Burberry union: the former's products are considered what the trade terms "affordable luxury," despite management talk about the brand, while Burberry is regarded as a legacy brand with a loftier profile. However, some of its efforts to look down its nose at some customers have been compromised by the decline in the value of the British currency, which means tourists in the U.K. find the products more affordable.

To be sure, Coach has evidenced its adroitness at managing acquisitions. Last year it bought the luxury shoe brand Stuart Weitzman for $574 million, and has already begun to wring some benefits out of the union.

If Coach does have any intention of proceeding with some pursuit of Burberry, it's going to have to sharpen its strategy, Kotter's Gersch said. "What are the benefits of any such merger, and how are they going to achieve them?" she asked rhetorically.

There could be benefits in the supply chain and distribution channels that could be exploited. Burberry could use an expanded footprint in North America just as Coach could benefit from a larger European market.

"If there's an intention to truly integrate these companies, what's going to be important is to engage both organizations equally," Gersch added.

For now, the talk of any Coach/Burberry amalgamation remains just that: talk. Coach's CEO Victor Luis spoke exclusively with The Street earlier this week and said regarding merger prospects, "In terms of acquisitions going forward for us, we have been pretty consistent in discussing our interest in three spaces: handbags and accessories, footwear and outerwear and other luxury retail categories secondarily."

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