The book, written by Jihad Uda, a university professor and senior member of the ruling National Democratic Party, appears to be the first public call from inside the NDP for 40-year-old Gamal Mubarak to succeed his father.
The book's publication follows the president's assurances in January that there would be "no hereditary transfer of power".
The publisher, Dar al-Huriya, said on Tuesday it had printed 20,000 copies of the book, Gamal Mubarak: Restoration of Liberal Nationalism, and was now distributing them to bookstores.
Uda describes in his book Gamal Mubarak, the younger of the president's two sons, as "emerging from inside the party, not forced upon it by a foreign influence," but acknowledges he lacks the legitimacy needed to take over the presidency.
Gamal Mubarak has not made a career in the army, the institution that has been supplying Egyptian presidents since the 1952 military coup that toppled the monarchy.
Uda lauds Gamal Mubarak's role in initiating efforts to reform
Husni Mubarak, 75, has never
named a vice president
and modernise the NDP last year, before the intensification of US pressure on Arab states to adopt democracy and free-market economies.
He praises Gamal Mubarak as "the most qualified" to be president based on his personality, his connections to the political establishment and his pro-US orientation.
These assets, he argues, are necessary for the younger Mubarak to "take over the presidency" and then push for a gradual change which would be homegrown and not "ready-made or imported."
Husni Mubarak, 75, has never named a vice president, the route he and his predecessor Anwar al-Sadat took to become head of state.