The book, 'Ikea Moving to the Future' (Ikea på väg mot framtiden), claims that Ikea founder Ingvar Kamprad and his three sons are at loggerheads over the money, reported the Swedish newspaper Dagens Industri (DI).
The three sons hired a star lawyer from the US to take on their 87-year-old father, a resident of Lausanne who declared earlier this year that he would be leaving Switzerland to return to his homeland after 40 years away.
The patriarch, noted for his frugality, moved to a municipality near the Vaud capital to escape high Swedish taxes.
His fortune was estimated in July at $44.6 billion francs ($48.9 billion) by Swiss business magazine Bilan, but Forbes in March put the figure at a more modest $3.2 billion.
The difference may be accounted for assets over which Kamprad controls but it is not clear if he owns.
The new book, which is has yet to be published, was penned by Lennart Dahlgren, the former head of Ikea in Russia, and researchers Stellan Björk and Karl von Schulzenheim.
The authors claim that the financial dispute can be traced back to 1982, when Kamprad registered Ikea in the Netherlands with the Dutch Stiching Ingka Foundation, but he kept the immaterial rights to the brand, which provided him a turnover-based compensation.
Kamprad's move only afforded him a tiny fraction of the proceeds from the company, but over the next 30 years, the sum increased to 20-30 billion kronor ($3.14 billion to $4.71 billion), the authors reckoned.
Legally, the funds belonged to the sons according to the book, something that led to a long fight within the family, which ended up with Kamprad senior falling ill.
No members of the family have commented as yet.