All news to Mr Melmoth, and untrue. But add a City whizz-kid, who had already bought some of the CWS's food factories three years ago, and the story seemed to have legs.
Andrew Regan, the 30- something high-flyer at the centre of the media frenzy that ensued, can go to hell, Melmoth says. "If ever we got rid of our farms, pharmacies and funerals, we might as well turn out the lights. I couldn't sell the idea of selling those things to the movement itself, let alone Mr Regan."
Regan, who was holidaying in the Caribbean last week, may also come to rue the speculation as the Stock Exchange investigates the leak. Shares in his latest vehicle, Lanica Trust, a bloated bubble of hot air in recent months, were suspended last week.
But for the Co-op some good may yet come of the odd turn of events. The CWS and the Co-operative Retail Society, the other large chunk of the movement, moved swiftly to quash the speculation. The joint response, and the fact the phones were buzzing again between the two, raised fresh hopes that the great inevitable might at last happen: a merger that will finally allow the Co-op to take on the Sainsburys, Tescos, Safeways and Asdas to which it has lost so much ground in the past two decades.
"It will happen, the question is just when. I have a sense that the pace will quicken over the next year or two," Melmoth says.
He enjoys a cordial relationship with Harry Moore, his counterpart at CRS, which helps. But it was not ever thus. On-off merger talks, started in 1981, last collapsed two years ago and the respective managements have been skirting the issue since.
Personalities, history, constitutions and culture were all at fault. But, as Melmoth is the first to concede, the bickering and peacock-style displays of pride ill befit the ideals of the Co-op's pioneers in Rochdale 150 years ago. For co-operative, read vituperative more often than not.
The Co-op still runs 3,500 shops across the land, more than 1,000 of which are owned by CWS and 550 by CRS. It runs Britain's biggest funeral business, handling a quarter of the country's burials every year. With 50,000 acres, it is our biggest farmer and one of the largest milk processors, with pounds 600m worth of milk, cheese and butter sales alone last year.
Co-op travel agencies are in the top five, the Co-operative Insurance Society (with funds of pounds 13bn) is in the top flight and the Co-op Bank is blazing the trail in armchair banking.
With many cramped stores of the sort long closed by Tesco and Sainsbury's, however, the Co-op is a long way from its heyday in the 1970s when Melmoth joined. Then it had around a fifth of the grocery market, against 7 per cent now.
Melmoth, an amiable man just turned 58, has the Co-op in his blood. His parents were members of the old South Suburban society in London - since taken over by the CWS - in the days when mothers hoarded dividend stamps by the hundred and guarded their pounds 1 membership jealously. His father, a Devon carpenter's apprentice by background, did well enough in the capital, however, to end up as a director of a London textile firm.
The fruits of this sent Melmoth to a public school, the City of London, where after 'A' levels he desperately wanted to be a journalist at first. National Service knocked those ideas out of him and, following a spell as a Royal Artillery lieutenant in Cyprus, he went into industry.
Over the next 16 years, Melmoth honed his trade as a chartered secretary, an esoteric profession which involved everything from taking the minutes to registering patents, negotiating the sale of chemical plant and directing strategy. His travels took him from BET to BOC, Fisons and finally Letraset - a freewheeling private firm where he was the only non-millionaire on the board.
He met his wife of 30 years, Jenny, a social worker, treading the boards in amateur dramatics in London, and they started a family. Then, in 1975, they were uprooted both culturally and geographically. When the job of company secretary at CWS in Manchester came up, the family jumped at the chance to quit the capital.
"We enjoy the ethos of the North," says Melmoth. "I've always been of the left, but as for culture shocks, it was the biggest of them all."
"It was very tough for me, going from a small go-getting entrepreneurial firm to a huge, strait-jacketed hierarchy. I was the minutes man, the company butler, if you like. It was all very inhibiting at first."
The CWS was founded in 1863 as the main supplier of goods and services to the 900 retail Co-op societies that blossomed and still existed a century later.
By the mid-1970s, however, the shape of the organisation and the movement was starting to change. Baling out the biggest Scottish society after a banking crisis in 1973 took the CWS into retail for the first time. It is a role, as rescuer of first resort, the CWS has performed many times since to become the biggest high-street Co-op with total sales of pounds 3bn last year.
As right-hand man to three chief executives, before landing the top job last November, Melmoth has been at the centre of consolidation. Now, because of competition or just plain bad management, fewer than 60 individual societies remain.
Most have jettisoned their own buying operations to join the CWS's Co- op Retail Trading Group (CRTG). This is the focal point of Melmoth's attempts - short of total merger - to forge a unified structure for sourcing, branding and direction to take on the competition.
"When I first came in, Tesco was still in Green Shield stamps and Sainsbury's was hardly north of Watford. Now it is admitted that we face the most formidable quartet of grocery multiples anywhere in the world," says Melmoth.
"We must button down our core food business on solid ground and not put down investment unless we get adequate returns."
Internally, the CWS has shaken itself up, building a cohesive regional structure from a loose set of fiefdoms. Four years ago it was in the red, after rescuing two more ailing societies. Profits last year, though, recovered to pounds 46m, more super-stores have been opened, smaller shops have been closed or refurbished and a new "Dividend" savings card is being rolled out, starting in Scotland.
It is perhaps a mark of the Co-op's slippage that years after most societies gave up stamps, Tesco stole a march last year with its loyalty card, the modern equivalent. The Co-op was not the only grocer to be wrong-footed; one dramatic casualty was Sainsbury's.
Melmoth, however, places great faith in the Co-op's dividend revival, which is different in targeting not the Kelloggs or Nescafes, but only its 4,500 in-house lines.
"This is intended to help boost our brand. It offers a 5 per cent dividend. Tesco and Sainsbury's cards are worth 1 per cent at most," he says. "They can go so far in stealing our clothes, but there is a limit."
Still, for Melmoth as with Tony Blair, modernisation has hardly gone far enough. The fault lines in the movement, the awkward voting structures, the rivalries are all still there.
The CRS, along with United Norwest, the Portsea Island and the Yorkshire Co-op, belongs to the Consortium of Independent Co-ops, a refusenik group outside the CRTG.
Melmoth hopes, through common sense and purpose, that all can be persuaded to migrate, if not merge.
But if the dream is achieved, how will the Co-op keep its identity when so many other mutuals - building societies and insurers - are shedding theirs in droves?
"We will remain the 'Responsible Retailer'. People will always recognise us as having a history of trading ethically. There is no doubt that has struck a chord," he says.
"There is a place for the Co-op. But there is no place for a badly managed Co-op. If we don't get our act together, we don't deserve to survive."