Sears Canada is beginning to brace itself for a possible bankruptcy.

The cash-strapped department store chain has begun to reach out to top law firms in Canada in a desperate search for restructuring advisers as it weighs a potential Chapter 11 filing, The Post has learned.

A bankruptcy filing isn’t imminent or even certain, sources cautioned.

Plus, the money-losing chain likely has enough inventory to get through the holiday season.

At the same time, billionaire Eddie Lampert — who as chairman of Sears Holdings controls Sears Canada through a 51 percent equity stake in the company — hasn’t yet given up on turning around the ailing chain, which has seen sales decline in each of the past six years.

Still, a bankruptcy law firm in Canada has received an inquiry from Sears Canada about being retained, sources close to the matter said.

Asked by The Post on Thursday about Sears Canada’s recent talks with bankruptcy lawyers, company spokesman Vincent Power said, “There is no truth to this.”

Lampert has tried — unsuccessfully so far — to sell Sears Canada. The investor is now scrambling to sell more of the chain’s best locations to raise cash outside of a court proceeding, sources said.

But with Sears Canada’s prospects as a business in doubt, the prospect of a piecemeal selloff of the retailer looks less lucrative.

As reported by The Post earlier this week, an auction by Chicago-based Sears Holdings of its 51 percent stake in Sears Canada failed to attract any bids in its second round.

That’s because prospective bidders in the auction run by Bank of America got spooked after getting a look at the company’s fast-deteriorating financials, sources said.

Now, it’s suppliers that are growing skittish about Sears Canada’s ability to pay its bills through the cash-intensive ramp-up to Christmas.

While the timing of any possible bankruptcy filing remains uncertain, insiders are increasingly concerned it could come at the start of the new year.

It didn’t help Thursday when Sears Canada said CEO Douglas Campbell will leave the company no later than Jan. 1 so that he can “tend to personal family issues.”

Lampert’s habit of selling off Sears Canada’s assets, including the sale of five top locations for $400 million last fall to landlord Cadillac Fairview, has put the chain in an increasingly tight position.

In its announcement of Campbell’s resignation, Sears Canada said it “remains committed to continue the strategy of optimizing productivity, realizing value from desirable assets, and creating a highly relevant retailer in Canada with a focus on rural and suburban locations.”

The company added that its board “is focused on maximizing total value. At the end of the year, the Board will review the appropriate level of cash for the Company, and any potential return of capital to shareholders, based on the performance of the company during the holiday season and the prospects for the business going forward.”

Separately Thursday, Fairholme Capital Management, one of Sears’ largest shareholders, said it was unable to reach a deal with real estate firm St. Joe to participate in a $400 million loan to Sears Holdings.