Billionaire Eddie Lampert’s bid to sell Sears Canada looks like a bust — and that’s bad news for Sears at home.

An auction of a majority stake in the Canadian retailer failed to attract any acceptable bids in its latest round, eliminating a potential near-term cash infusion for Sears Holdings that could have exceeded $750 million, The Post has learned.

Indeed, a flopped auction of the 62-year-old Canadian chain early this month was a key reason that the corporate parent of Sears and Kmart was forced last week to take out a $400 million loan as it prepares for the crucial holiday season, sources said.

Last week’s emergency loan to Sears has attracted scrutiny, as it is being issued by none other than Lampert, the chairman of Sears, whose hedge fund ESL Investments demanded 25 of Sears’s best store locations as collateral.

“Things have not turned out like Eddie hoped, and now he’s getting desperate,” said Mark Cohen, a professor at Columbia Business School who was Sears Canada boss before Lampert took control.

Sears burned nearly $1 billion in cash during the first half of the year, leaving it with just $863 million on its balance sheet for the Christmas season.

“This is a late-stage death spiral for both Sears and Sears Canada,” Cohen said.

Asked about the flopped auction, a Sears spokesman said, “We continue to explore alternatives to recognize value from our equity stake in Sears Canada and from our Sears Auto Center business.”

The $400 million loan “provided us a more predictable source of funding and financial flexibility through the holiday season,” he added.

The Chicago-based retailer hoped to raise at least $765 million from its 51 percent stake in Sears Canada, shares of which on the Toronto Stock Exchange closed Friday at $13.96, giving it a total market value of $1.42 billion.

Prospective bidders, however, balked in the second round of the auction after getting a closer look at Sears Canada’s financials, sources said. A key concern was forecasts for slumping sales and widening losses.

“They’ve got valuable assets,” said one source, citing dozens of store locations that are still envied by competitors. “But you’ve got to weigh that against the rate that they’re burning cash, which is accelerating.”

Sears Canada’s losses are widening after Lampert sold off a dozen of the chain’s best locations, including a $400 million sale of five stores last fall to landlord Cadillac Fairview.

Lampert could be forced to sell off additional Sears Canada locations in the coming months — a move that would further accelerate the cash bleed, sources said.

Among a handful of bidders for Sears Canada this summer was Sycamore Partners, a New York hedge fund that has scooped up retail companies Jones Group, Talbots and Hot Topic.

But while Sycamore had initially expressed interest in taking over Sears Canada’s business, it later weighed a liquidation bid before abandoning the process altogether, sources said.

A spokesman for Sycamore declined to comment.

As reported by The Post last week, suppliers and trade lenders including CIT are tightening credit for Sears amid concerns that the retailer’s widening losses will leave it short of cash to pay its bills as the holidays shift into high gear.