A court in October ordered Alaa Mubarak and Gamal Mubarak to be released after having taken into account the time spent in jail since their detention in 2011.
The prosecution has filed an appeal in the Court of Cassation against the release order, which has not been implemented, the judicial official said, without specifying when the petition was filed.
State news MENA also reported the prosecution's move to file the appeal.
Their lawyer, Farid al-Deeb, argued in October that his clients should be allowed to go free because of time already spent behind bars.
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In May, a court sentenced them to three years in prison each for having embezzled 125 million Egyptian pounds (USD 16 million) from funds meant for the maintenance of presidential palaces.
In January, Alaa and Gamal Mubarak were released briefly after their pre-trial detention period expired, but they were re-arrested in May after the verdict was pronounced.
His sons, both in their early 50s, still face a separate trial for alleged stock market manipulation.
Following Mubarak's ouster, many former regime figures were arrested and tried, including on charges of corruption, but most have been acquitted.