Prosecutors previously interrogated the two over claims they manipulated Egypt's stock exchange and made money from the country's debt settlement, al-Masry al-Youm reported.
The brothers are now in Tora Prison, awaiting a corruption trial along with their father, who is also charged in the deaths of protesters calling for his ouster. If new charges were filed, they would be heard in a separate case, prosecutors said.
Investigators also said the appointment of Gamal Mubarak to the board of the Arab African Bank is a violation of the law.
A senior judicial official told al-Masry al-Youm prosecutors would investigate other officials implicated in the potential new charges, including former Prime Minister Atef Ebeid, former Deputy Prime Minister Youssef Wali, former Finance Minister Youssef Boutros-Ghali and former Agriculture Minister Amin Abaza.