BJ's Wholesale Club Inc. has hired Morgan Stanley to help it sell the company and plans to run an auction for the sale, Bloomberg reported Wednesday, citing people familiar with the situation.

The plan to run an auction comes after the warehouse club operator received an offer from private equity firm Leonard Green & Partners LP in recent months, Bloomberg reported, citing three people familiar with the situation.

BJ's shares jumped 9 percent to $45.84 following the report. The company declined to comment.

The sale of the No. 3 U.S. warehouse club operator could command as much as $3 billion, the New York Post said earlier on Wednesday.

In July, a fund run by Leonard Green said it had taken a 9.5 percent stake in BJ's and that it may propose taking the company private.

Green and Morgan Stanley could not immediately be reached for a comment.

BJ's has struggled to expand due to the earnings hit that comes with opening in new markets, Janney Capital Markets analyst David Strasser said in a research note.

"We envision a scenario where BJ management, as a private company, takes the earnings hit in the near term by entering new markets, and then grows square footage by predominantly filling in these markets, providing a sustainable square footage growth story and a solid exit strategy to go public again," Strasser said.

Leonard Green has about $9 billion in equity capital under management. Founded in 1989, it has invested in 51 companies with aggregate value of $43.4 billion.