Arthur S. Demoulas discussed a sale of his family’s stake in Market Basket with private equity company Cerberus Capital Management in the spring of 2011.

Boston.com confirmed the discussed deal with multiple sources with direct knowledge of it.

The discussions were not said to have gone particularly far, but reached the point of a term sheet, spelling out what a deal would have looked like. The new information indicates that Arthur S. Demoulas has at least considered selling the company to private equity, if he could arrive at a controlling stake in Market Basket, since before he gained control of the chain last summer.

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The proposed Cerberus deal would have depended on Arthur S. Demoulas being able to offer better than 50 percent of the company, according to a source who shared information on the condition of anonymity. The path to doing so would have likely required his sister-in-law Rafaele Evans to side with him and agree to a sale, the source said.

At the time, Evans did not support Arthur S. Demoulas. Last summer, however, Evans began to vote in concert with him among shareholders, giving him de facto control of Market Basket. That began the process that eventually led to the firing of his cousin, former Market Basket CEO, and still-shareholder, Arthur T. Demoulas. Arthur T.’s firing has sparked worker protests and wide-scale boycotts of the company.

Current Market Basket co-CEO Felicia Thornton was the CFO of the Albertsons supermarket chain in 2006 when that company was acquired by multiple parties, including Cerberus. Boston.com does not have any evidence that Cerberus, which in recent years has bought the grocery chains Shaw’s and Safeway, is still interested in buying Market Basket, or that Market Basket’s board is looking to make a deal with Cerberus.

The financial details of the discussed deal are not clear, but a source says Cerberus valued the real estate owned by the company. According to The Boston Business Journal, Market Basket owns more than 15 million square feet of property in Massachusetts.

The Boston Globe late Thursday night reported there may be several suitors for Market Basket, including private equity companies and rival grocers, and that the company has fielded offers. The Globe said that it is not clear whether recent events at the chain have led to offers being withdrawn.

Many employees have held since Arthur S. gained control of the company last summer that they expect him to try to sell it.

Another potential buyer is Arthur T. himself, who has offered to buy out rival family members for their 50.5 percent stake in an effort to regain control of the company and end the turmoil it has faced since he was fired. On Friday, the board released a statement saying it would consider Arthur T.’s offer, as well as other offers.

Arthur S. Demoulas did not respond to requests for comment before this article was published. Cerberus declined to comment for this article.

Check out more Boston.com coverage of the Market Basket saga here.