A private investment management company gave major bookstore chain Barnes & Noble Inc a conditional offer to buy 51% of the company that remains the only major player in the national bookstore market, the Los Angeles Times reported.

G Asset Management, a New York-based firm, proposed to buy the firm for $22 per share, saying that the offer was at a 31% premium than the most recent closing price of Barnes & Noble which was pegged at $16.78 a share, the report said.

G Asset Management said their bid hinges on various conditions, such as the fulfillment of due diligence, ability to secure financing and the result of the negotiations. The investment management firm said that the national bookstore chain is "substantially undervalued in its current form." Barnes & Noble stock rose 5.8% to $17.76 a share in mid-afternoon New York trading, the report said.

According to G Asset Management, if the major chain does not agree on its bid to acquire a controlling stake in the entire firm, it will make another proposal to purchase a 51% stake of the company's Nook e-reader segment. The investment firm said its $5 per share offer for the e-reader would be valuable for shareholders since it would detach Nook from the retail and college bookstores operations of Barnes & Noble which are raking in profit, the report said.

In November last year, G Asset Management offered $20 a share for 51% of the national bookstore chain. Barnes & Noble Chairman Leonard S. Riggio also dropped his plans to purchase the bookstores of the company in 2013, the report said.

Last month, Barnes & Noble said that it was able to post sales of $1.1 billion in the nine-week holiday period that ended on December 28. This represented a 6.6% decline from its sales the year before. Revenue for Nook, however, declined 60.5% to $125 million year on year, the report said.