NEW YORK — Cerberus Capital Management LP’s pursuit of grocery chain Supervalu Inc. — which owns all Albertsons stores in Idaho — has stalled because the private-equity firm has had trouble obtaining the funds for a leveraged buyout, said people familiar with the matter.

Potential lenders are balking because they’re concerned over how the Eden Prairie, Minn.-based chain will manage the increased debt load as revenue shrinks, said the people, who asked not to be named because the process is private. Lenders are also pressing Cerberus to put more money into the deal than the firm is willing to, said another person.

Without a sale to Cerberus, Supervalu risks having to restructure its grocery chains on its own or sell individual assets, the people said. That may pose a challenge because the struggling retailer would face big tax payments for selling the assets, the people said.

Peter Duda, an outside spokesman for Cerberus at Weber Shandwick, declined to comment on the process. Mike Siemienas, a spokesman for Supervalu, declined to comment on negotiations with Cerberus.

Supervalu’s market value has shrunk as the grocer lost more than $2.5 billion over the past two fiscal years, hurt by increasing competition from discounters and costs to run stores. For its most recent quarter, ended Sept. 8, the third-largest U.S. grocery chain posted a net loss of $111 million, or 52 cents a share, compared with net income of $60 million, or 28 cents, a year earlier. Sales fell 4.6 percent to $8.04 billion in the quarter.

In July, Supervalu said it was working with Goldman Sachs Group Inc. and Greenhill & Co. to review options. The company attracted interest in parts of its business from private-equity firms KKR & Co. and TPG Capital, as well as from billionaire Ronald Burkle, people with knowledge of the matter have said.