The magazine has a long history of publishing short stories by such novelists as Arthur C. Clarke, Ian Fleming, Vladimir Nabokov, P. G. Wodehouse, and Margaret Atwood. Playboy features monthly interviews of notable public figures, such as artists, architects, economists, composers, conductors, film directors, journalists, novelists, playwrights, religious figures, politicians, athletes and race car drivers. The magazine throughout its history has expressed a libertarian outlook on political and social issues.
Playboy declined to comment. Golden Gate Capital, which is in joint talks with Griffiths, were not immediately available for comment.
The company is also in separate talks with Iconix Brand Group to sell itself, sources told Reuters on Thursday.
Iconix, which owns and licenses clothing brands such as Candies, Joe Boxer, and Rocawear, wants to bring in a publishing partner to buy Playboy magazine while it would keep the licensing part of the company, one of the sources said.
At this point, the talks with Griffiths and Golden Gate are separate from those with Iconix, the source said.
Playboy's shares were up 6.6 percent at $4.34 in Friday's trading on the New York Stock Exchange. The stock rose 41 percent on Thursday, following initial news of the talks with Iconix.
Based on Thursday's closing price, the company had a market cap of about $116 million.
In addition to its well-known adult magazine, Playboy also has TV operations and a licensing business based on its "bunny ears" logo.
Golden Gate owns investments across several sectors, including media, transportation and healthcare.
Playboy magazine's sales have suffered in recent years as more people get adult entertainment on the Internet, and as advertising sales have fallen at most U.S. magazines and newspapers.
Before the stock jumped on Thursday, Playboy shares had lost about 75 percent of their value over the past two years.
The company has been looking for a buyer for months, even before the appointment of a new chief executive in June, when Scott Flanders replaced Christie Hefner, the daughter of the magazine's founder Hugh Hefner.