The head of a sizable hedge fund is eyeing bringing the Kenmore and DieHard brands out of the Sears bankruptcy — but it is not clear if he can pry them away from company honcho Eddie Lampert, The Post has learned.

This hedge fund has signed a confidentiality agreement with Sears to study the brands, according to a fund source who requested anonymity.

News of the interest comes as Sears considers bids on Monday for its assets, including a last-ditch $5 billion-plus offer from Lampert, which includes an extra $600 million for additional assets, including 57 real estate properties.

Liquidators also are expected to bid for Sears, but they have no interest in the Kenmore and DieHard brands, sources said.

The hedge fund’s Kenmore-DieHard bid would be contingent on the rejection of Lampert’s revised bid, the source said.

That scenario may introduce other problems, though.

Creditors will be claiming Lampert’s hedge fund firm, ESL Investments, controlled Sears and loaned money to Sears entities to get an unfair advantage over them in what is called “equitable subordination.”

“If the Sears creditors don’t want Eddie’s bid, they will be in court forever fighting Eddie,” the hedge fund source said.

“Sears’ creditors want cash but frankly, those brands are tied up with the debt Eddie put on the brands,” the hedge fund source said. There is about $900 million of debt associated with DieHard and Kenmore, according to public filings.

“ESL could object to the sale,” distressed asset expert Adam Stein-Sapir told The Post. “A buyer could find itself in the middle of all of these parties who have an interest in those assets, including the creditors, Sears and ESL.”

“Eddie has debt to these entities, and he has a claim,” a source close to Sears said.

Lampert last spring offered $400 million for Kenmore but could not get his deal completed, partly because the government’s Pension Benefit Guaranty Corp. wanted a share of the proceeds, as it is helping to cover benefits for 100,000 Sears retirees.

Sears owns the brands through an entity — Sears Reinsurance Co. — that’s not part of the bankruptcy and which has outstanding loans to ESL, according to public filings.

Sears declined to comment.