LEBANON, TENN. — Cracker Barrel Old Country Store’s largest shareholder has suggested the restaurant and retail chain pursue a sale — and he’s willing to bid.

In a Dec. 24 letter to Cracker Barrel chairman James W. Bradford, activist investor Sardar Biglari said his San Antonio-based investment firm, Biglari Capital Corp., which owns nearly 20% of Cracker Barrel’s outstanding shares, is “willing to lead the process by submitting a bid” for the company to improve its earning potential. But because Tennessee law restricts such a transaction, Mr. Biglari also wants the board’s help in seeking an amendment to the state law to enable the deal.

“We believe Cracker Barrel’s assets would be far more productive under our leadership than in the hands of present leadership,” Mr. Biglari wrote. “Thus, we are willing to purchase the business because we perceive a significant upside under our management. But other sophisticated buyers also should have the opportunity to bid for the company.”

He said his firm is willing to buy the business because he believes its current management lacks the “entrepreneurial mind” needed to create substantial value and that the company’s “earning power is far too low in your hands.”

“To illustrate, we had to drive the board and management to license products to third parties,” Mr. Biglari said. “Now that you see the benefits to the business, management claims the idea was part of its plan. But we have no interest in gaining credit; our interest lies in making money. Yet it is obvious you will have difficulty growing earnings through operating performance henceforth. We are convinced you are leaving a ton of value on the table.”

Another example of poor judgment, he added, was Cracker Barrel’s recent handling of the “Duck Dynasty” controversy. The company had pulled merchandise related to the television show following an incendiary interview from a cast member but quickly resumed selling the products after receiving complaints from customers.

If Cracker Barrel is not willing to sell, Mr. Biglari said the company should consider a share repurchase program.

“We would consider selling our entire position because we would not want to leave our money in your care,” he said.

Mr. Biglari said his firm has been working with an investment banking firm to arrange financing for the transaction and is prepared to collaborate with Cracker Barrel to amend the Tennessee law.

“Should the board refuse to take meaningful steps to engage in an extraordinary transaction, including the public announcement of its commencement of such a process, we then intend to exercise any and all rights and remedies at our disposal, including a call for a special meeting of shareholders,” Mr. Biglari said.

During the annual meeting of shareholders in November, Cracker Barrel shareholders rejected Mr. Biglari’s nomination to the board as well as a non-binding advisory proposal from his firm on a $20-per-share special dividend.

For the fiscal year ended Aug. 2, the company’s net income increased 14% to $117,265,000, equal to $4.95 per share on the common stock, up from $103,081,000, or $4.47, during the previous fiscal year. Sales were $2,644,630,000 for the year, up 3% from $2,580,195,000 during the prior year.