The brothers had gathered an impressive team, including US bankers Salomons, blue-chip broker Cazenove and public relations guru Sir Tim Bell, to advise on the listing here and on Wall Street.
The news comes amid growing doubts over Liberty Publishing, Mohamed al- Fayed's would-be media empire, following the surprise walk-out nine days ago of chief executive John Dux along with his entire staff.
It also marks the end of ambitions to raise up to pounds 500m of new money to fuel Harrods' expansion around the world.
"There are no plans to take the company to the stock market in New York or London now or in the foreseeable future," a Harrods spokeswoman said.
The firm did not elaborate, but the complexity of unravelling the brothers' wide business interests and the obligations of disclosure in the public arena are thought to have played a part.
The Fayeds bought Harrods' then owner, House of Fraser, for pounds 573m in 1985 and waged a long war against Lonrho founder Tiny Rowland for control.
A report in 1988 by the Department of Trade and Industry found, however, that they had dishonestly misrepresented their origins, wealth, business interests and resources during the battle.
Analysts had always dismissed the pounds 2bn price hopes as fantasy. Last year Harrods Holdings made profits of pounds 68m on sales of pounds 577m - respectable enough, brokers say, but implying a 60 per cent premium to valuation yardsticks for Harvey Nichols, which was floated last year.
"Two billion was always a bit rich. For prestige they might have been up near there, assuming no historic baggage, but of course with Harrods there is," one leading retail analyst said.
Mr Dux's exit, meanwhile, signals an end to the Fayeds' ambitions to create a major media force.
Attempts to buy a national newspaper - first Today, then the Observer and latterly the Independent - have failed and there is doubt now over the relaunched Punch magazine and Liberty Radio.
His departure reduces to one the gang of three drafted in to head Liberty, following the removal of columnist Peter McKay as Punch's editor last year.
Stewart Steven, Liberty's chairman, former editor of the London Evening Standard and Punch's new editor, is the sole survivor.
According to colleagues, Mr Dux had become unhappy with the lack of progress over the last six months. Punch has already absorbed some pounds 13m, while achieving a readership of barely 60,000.
Liberty Radio, bought for pounds 3m out of the unsuccessful feminist station Viva, is still struggling to find an audience and a bid for London's last FM licence came to nought last year.
Last week, Mr Steven claimed Mr Dux's exit came as no surprise. "John and I met last month to discuss the future of Liberty," he said. "The job in hand was largely an acquisitive one. The company has no further ambitions in that line for as far into the future as we can see, so we decided there was little point in him staying around."
Mr Steven declined to comment on his own plans, but colleagues say he will also step down by August this year, come what may.Reuse content