The ownership of Cub Foods may be up in the air, but its future is not, leaders of the Twin Cities’ biggest grocery store said.

“Cub will be Cub. We’re not closing them,” said Anne Dament, who leads Stillwater-based Cub as executive vice president of parent firm Supervalu Inc.

Cub went on the block after United Natural Foods Inc. purchased Supervalu, in a $3 billion deal that closed last month, and said it would sell Cub and the other grocery chains that provided about 30 percent of Supervalu’s revenue.

The process of finding a buyer is likely to take several months, but executives at Cub, Supervalu and United Natural Foods have started. They aim to sell the 78-store chain as one unit rather than in pieces.

“Ideally, we would find one buyer,” Dament said in an interview last week.

In 2014, Milwaukee-based Roundy’s decided to sell its approximately 30 Rainbow stores in the Twin Cities and did so in piecemeal fashion. Supervalu, Jerry’s and Lunds & Byerlys each bought some Rainbow locations.

To help a Cub deal along, executives also signaled a willingness to let go of Cub as a customer of Supervalu’s wholesale business, though they would prefer to keep it. Many possible buyers of Cub — particularly large chains such as Albertsons, Hy-Vee and Kroger — use different wholesalers or operate their own supply operations.

“Where appropriate, we will separate supply agreements from the sale of the banner in order to more expeditiously move” to sell Supervalu’s groceries, Steven Spinner, chief executive of UNFI, said in July when its purchase of Supervalu was first announced.

Last week, Supervalu spokesman Jeff Swanson said that Cub is an important customer to Supervalu and executives hope to continue to supply Cub after it is sold. “But we can’t speculate until the process plays out,” Swanson said.

For a prospective buyer, the key to Cub’s appeal is the 46 stores in the Twin Cities that reach one out of four metro-area grocery shoppers and have led the market for decades.

Supervalu has remodeled more than half those stores since 2016 and has not let up on that effort since the UNFI deal came together. Last Thursday, the company held a grand reopening for the latest Cub to get a makeover, in Chanhassen. Besides a new popcorn shop and an expanded grab-and-go section, the store has a new coffee shop, called Refresh, that offers Caribou Coffee with payment on the honor system.

Remodelings of stores at St. Paul Midway and Maplewood West are underway. And construction on a smaller, urban store near 46th and Hiawatha in Minneapolis is scheduled to be complete by spring.

Kroger, the nation’s largest grocery chain, is widely seen as a prospective buyer for Cub. The Cincinnati-based company has no stores in Minnesota and it has a track record of acquiring regional chains and operating them under existing names.

In 2016, Kroger added 166 Roundy’s stores and kept the names Roundy’s, Mariano’s, Pick ‘n Save, Copps and Metro Market. Kroger has also purchased banners such as Ralphs, Pay Less, Harris Teeter, Fry’s and Food 4 Less.

Kroger spokeswoman Kristal Howard said in an e-mail, “We don’t comment on rumor or speculation.”

Hy-Vee, the Iowa-based grocer that entered the Twin Cities market three years ago and has grown to 10 locations, has said it’s not interested in buying Cub, though it opened a store in a former Cub location in Plymouth just last week.

“The Plymouth store was not part of a strategy. It came available and so we decided to pursue it,” said Randy Edeker, chief executive of Hy-Vee. “I’m not going to put Hy-Vee at risk. ... We’re going to stay on a steady growth plan that’s manageable.”

Hy-Vee plans to open two large stores in the Twin Cities next year and has announced plans for five more.

Representatives from Fresh Thyme and Meijer have also said acquiring Cub stores is unlikely. Fresh Thyme, which has seven Twin Cities stores, had originally planned to have a dozen by 2020, but communications manager Kaitlyn Gerts said it plans only one new Minnesota store, in Rochester, next year.

Meijer, a Michigan-based superstore chain, had plans to enter the Twin Cities in 2016 with sites under contract in Brooklyn Park and Lake Elmo. Now, the company has no plans for stores in Minnesota, Frank Guglielmi, senior director of operations, said.

Local retailers such as Lunds & Byerlys, Coborn’s, Kowalski’s, and Festival are all supplied by Supervalu and could pick off a few Cub stores, though their market saturation is fairly mature.

About 70 percent of the company-run Cub stores are in leased spaces, which leaves open the possibility that, in a pinch or economic downturn, United Natural Foods could wind them down quickly.