The proposal came from Gopinath Munde of the ruling Bharatiya Janata Party, who says the book, issued in 1986, demeans the 17th century warrior Shivaji.
The book, "The Discovery of India," was first published in 1940 and is considered a classic work.
In 1986, Nehru's grandson and India's then Prime Minister Rajiv Gandhi released a new version of the book which is under fire now.
Nehru belonged to the Congress Party, which is pitted against the BJP in the upcoming federal elections.
The BJP says the book tarnishes the image of Shivaji, who is revered in Munde's home state Maharashtra.
Munde sought an apology from Nehru's Italian-born grand daughter-in-law Sonia Gandhi, who is president of the Congress party.
Several writers have denounced the attack on a book, saying Nehru was a serious intellectual and a statesman."
The Congress Party has also criticized the demand, which could be an issue in the elections.
Beyonce flaunts bikini body, Blue Ivy in vacation pics
Gal Gadot cast as Wonder Woman for 'Batman vs. Superman'