The news sent shares up nearly 9 percent in midday trading.
Riggio disclosed in a regulatory filing Monday that he wants to acquire the company's stores and website, but not the business that makes the Nook e-reader or the company's college bookstores. No price was disclosed.
It's the latest attempt by a company founder to take back control of all or part of a company he founded. Best Buy's co-founder Richard Schulze is mulling a bid for the electronics retailer, and Michael Dell earlier this month announced a $24.4 billion deal to take the namesake computer company he founded private. The deals are a way executives can have more control over companies without the need to run everything by shareholders.
"When you've got control outside public eye or public market, you can invest and translate your strategy at your own pace," said Morningstar analyst Peter Wahlstrom.
Riggio, who founded Barnes & Noble in the 1970s and helped it expand its "big box" presence, is Barnes & Noble's largest shareholder, with nearly 30 percent of the company's shares. (While Riggio didn't found the original Barnes & Noble store in New York, which opened in 1917, he bought the store and brand name in the 1970s to create the current-day company.)
Barnes & Noble said the offer will be considered by a committee of three independent directors. But there is no set timetable for the process.
The New York-based bookseller has been struggling to find its place in the retail landscape as more readers have shifted to electronic books and competition has grown from discount stores and online competitors.
It has invested heavily in its Nook e-book readers and digital library and struck a deal with Microsoft last April to create a Nook subsidiary.
But the Nook faces tough competition from other devices like Apple's iPad Mini, Amazon's Kindle and Google's Nexus tablet.
Earlier this month, the company said it expects Nook media revenue of less than $3 billion. It also anticipates a loss for the unit before interest, taxes, depreciation and amortization to exceed the $262 million loss recorded in its 2012 fiscal year.
This follows a report from the retailer in January that its Nook unit revenue fell 12.6 percent to $311 million during the critical holiday period. Overall sales during the holiday period fell 10.9 percent at bookstores and online compared with a year ago. Barnes & Noble is scheduled to report third-quarter results Thursday.
The filing with the U.S. Securities and Exchange Commission said Riggio will seek to negotiate a price with Barnes & Noble's board and pay for the deal with cash and debt.
Riggio is making the offer in order to facilitate the company's review of its strategic options for separating its Nook business, according to the filing.
Morningstar's Wahlstrom said the deal makes sense considering the retail side of the business has been overshadowed by investments needed for the Nook business.
"The retail business for Barnes & Noble is mature-slash-declining, but it's profitable," he said. "The company has done a good job executing amid a pretty challenging environment."
Wahlstrom added that the move by Riggio was not unexpected and has been a possibility for years. His large stake in the company and history would likely make finding any extra needed financing not much of a problem, he said.
"Riggio feels like he can run it better than just about anyone else, and with four decades of operating history there's not much reason to believe that he can't," he said.
Barnes & Noble operates 689 bookstores in 50 states and 674 college bookstores.
Shares rose $1.18, or 8.8 percent, to $14.69. Its shares have traded in a 52-week range of $10.45 in mid-April to $26 later that same month.