Barnes & Noble was once the Goliath of the book-selling business. Now, next to Apple and Amazon, its falling sales and plan to close 20 stores a year makes it look more like a struggling David armed only with a slingshot.

Barnes & Noble's weakening financial position makes the company vulnerable to takeover offers, and it received one on Monday. Barnes & Noble said in a regulatory filing that its founder and chairman, Leonard Riggio, proposed buying the company's bookstore business and its barnesandnoble.com domain. Riggio will not make an offer for the Nook e-reader business, according to the company. He already owns 29.8% of the company.

It is not yet known how much Riggio plans to offer, or whether he has arranged the cash and bonds to pay for it. The company indicated in a filing that the deal is subject to negotiation of Riggio's specific financial terms, including terms of whatever financing he can gather.

Riggio could well end up with a bargain. The bookstore business of Barnes & Noble could be worth only about $484.5m, according to estimates by Stifel Nicolaus analyst David Schick based on the company's sales over the past 12 months.

Schick previously noted that the Nook business – which accounts for 8.5% of Barnes & Noble's total revenue – is worth about $1.79bn. Barnes & Noble controls about one-third of the market in US ebooks, according to the company's estimates.

Barnes & Noble stock is currently trading at around $14.78 a share, giving the company a market value of $867.4m. Stock prices are only one measure of a company's value, however – alongside sales and profits – and when when companies break up, their parts are sometimes worth more than the value of the whole. That is why many numbers are likely to circulate about Barnes & Noble's true value over the next few months.

Barnes & Noble has been struggling with a darkening financial picture. Its bookstore sales fell 10.9% compared to January 2012, while Nook sales declined 12.6% in that time.

Over the past year, Barnes & Noble has sold off ownerships in its Nook e-reader business and announced a plan to shut down about 20 stores a year, leaving it with about 450 stores in the next decade.

The kind of deal Riggio is proposing for Barnes & Noble is known on Wall Street as a "management buyout", in which a current CEO or executive makes a deal with banks and private equity firms to take over his own company.

Last month, the CEO of computer-maker Dell, Michael Dell, offered $24bn for the company with the help of private equity firm Silver Lake. The deal quickly came under criticism from some big investors suggesting Dell's offer was too low, which illuminated why these types of deals can often be controversial. Shareholders who already own stock become suspicious that a CEO or chairman can cut a sweet deal for a struggling company.

Newcomb Stillwell, a partner with law firm Ropes & Gray who advises on MBOs, said that once the Riggio bid is on the table, it could invite other bidders if the price isn't high enough.

"It's universally the case that these transactions are structured in a way that other bidders have an opportunity to bid after the original deal is signed up," Stillwell said. "If the price is low, people will show up to pay a higher price."

It's not clear what other bidders would be interested in Barnes & Noble. Its biggest rival, Borders, liquidated in 2011.

"The economics are against the print book industry," said Roger Kay, the founder of Endpoint Technologies Associates. He recounted a visit to a Barnes & Noble recently. "I did note that the Nook area was not just abandoned, but you don't get the sense you do in Apple stores of people kicking the tires."

"Now we're all in our splendid isolation reading our Kindles," Kay said.

Barnes & Noble started signalling last year that it would spin off its Nook business. In January 2012, Barnes & Noble announced it would look for ways to "unlock the value" of the Nook, which competes with readers against Amazon's sweeping Kindle franchise and Apple's iTunes. Barnes & Noble has a fraction of their reach and resources; Apple has a market value of $421bn and Amazon is worth $120bn.

Kay said that even though the Nook business has not been a big winner for Barnes & Noble, it had to try to create a competitor to Apple and Amazon.

"I think it was inevitable," he said. "They had to make a go of it. They had to try to throw a grappling hook and climb on. If they just stuck with brick and mortar physical books, it would have just been slow strangulation."

Since making its announcement last year, Barnes & Noble has sold off portions of the Nook business to other companies. Last year, Microsoft invested $300m in the Nook business in April and owns a stake of 16.8%, and educational publisher Pearson poured in $89.5m for a 5% stake in December.

In a conference call with analysts in January, Barnes & Noble CEO William Lynch said the company would grow the Nook. "The Nook business will scale in 2013," he promised.