Ahmed Shafiq, who has been living in the United Arab Emirates since losing the presidential election to Mohamed Morsi in 2012, was tried in absentia.
Gamal and Alaa Mubarak have been involved in a series of trials since their father’s fall from power.
All three men are still facing other corruption charges.
Ten other defendants were also cleared in Thursday’s verdicts in Cairo.
The case examined whether Ahmed Shafiq had enabled the Mubarak sons – both of whom were prominent businessmen – to buy land belonging to the Egyptian pilots’ association at a cheaper price than the market rate.
Egypt’s Al Ahram reports that the verdict in the second corruption case against Ahmed Shafiq will be announced later on Thursday.
Egypt’s former President Hosni Mubarak is being held under house arrest following his release from detention in August.
His retrial on charges of complicity in the killing of demonstrators in 2011 is under way, after his conviction in June 2012 was overturned on appeal in January 2013.
Hosni Mubarak is also charged in a further three corruption cases.
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