Aziz and two other members of the former regime of Saddam Hussein were sentenced to death in October for their roles in the persecution of Shiites in the 1980s. The sentence sparked international calls for leniency, though Washington said the matter was an Iraqi affair.
Giovanni Di Stefano, a lawyer representing the interests of the former leader from Italy, issued an eight-page appeal to Talabani for a presidential pardon for his client.
Di Stefano points to a series of constitutional issues that he says absolves his client of wrongdoing for matters related to so-called ethnic cleansing in Iraq.
"It is thus necessary that in all democratic societies where the judiciary potentially or even remotely fail the constitution, the president is duty bound to intervene," the appeal reads. "The powers of pardon are granted to ensure that injustice does not occur."
Leaders from the Vatican, Moscow and Greece have called on the Iraqi courts to call off the hanging of Aziz, who was the only Christian member of Saddam's regime.
Aziz, who suffered a stroke in January, has less than 30 days to appeal his sentence, though family members said he is resigned to his fate.
Talabani last week told reporters from Paris that he wouldn't sign the execution warrant for the former minister.