The proposal for Barnes & Noble would be for $22 a share, which would value the chain at $1.32 billion. The current offer is a sweetened version from G Asset Management's proposal in November, which valued the bookstore chain at $20 a share.
Alternatively, G Asset Management has proposed to acquire 51 percent of the Nook segment, valuing the segment at $5 per share.
Shares of Barnes & Noble finished up more than 5 percent on heavy volume.
Barnes & Noble did not provide a comment to CNBC, but confirmed that it had received the offer.
In 2012, Microsoft invested $300 million in the Nook unit for a 17.6 percent stake, valuing the division at approximately $1.7 billion. And in late 2012, Pearson took a 5 percent stake in Nook for $89.5 million.
Barnes & Noble is slated to post quarterly earnings next Thursday.
-By CNBC's JeeYeon Park. Follow her on Twitter @JeeYeonParkCNBC
image: © Abhi Sharma