Bookseller Barnes & Noble Inc
A settlement could be announced soon, possibly within the next 24 hours, according to the source who also cautioned that the talks could also fall apart.
The settlement would potentially involve adding three directors to the nine-person board, the source said.
The news came a week after Barnes & Noble, the largest U.S. bookstore owner, put itself up for sale, drawing interest from several private equity firms.
The talks between Burkle and Barnes & Noble were earlier reported by the New York Times and the Wall Street Journal.
Burkle's investment firm Yucaipa Cos recently owned 19.6 percent of Barnes & Noble stock.
The billionaire had sued in Delaware Chancery Court to void the New York-based company's poison pill that he said entrenches the founding Riggio family, and makes it harder for him to buy more stock or mount an effective proxy contest.
The source said that under an accord, Barnes & Noble will eventually give up one director.
The source said with a settlement, Burkle would withdraw the lawsuit, agree not to start a proxy fight, and support the company's director candidates in 2010 and 2011.
According to the Journal, one independent director expected to be added is Stephen Bollenbach, a former Hilton Hotels chief executive who is now chairman of KB Home
At the trial, Burkle testified that Yucaipa had in October 2009 considered, but then decided against, pursuing a $25 per share buyout bid for Barnes & Noble. He said he considered that a waste of time, given the Riggio family's effective control of 38.2 percent of the stock.
Leo Strine, the Delaware vice chancellor, is expected to rule soon in the case.
Barnes & Noble and Yucaipa did not return requests for comment. Both declined to comment to the Journal. Mary Ellen Keating, a spokeswoman for Barnes & Noble, and Frank Quintero, a spokesman for Yucaipa, declined to comment to the Times.
Shares of Barnes & Noble closed Wednesday down 50 cents at $14.48 on the New York Stock Exchange.
(Reporting by Sue Zeidler in Los Angeles, Jonathan Stempel in New York; Editing by Muralikumar Anantharaman and Valerie Lee)