The man who served Saddam Hussein as both foreign minister and deputy prime minister was sentenced to death October 26 for his role in persecuting Shiites and the crackdown on Iraqi Kurds.
Talabani told the international news channel France 24 while visiting Paris that he is personally opposed to capital punishment.
"I will not sign Tariq Aziz's death sentence," he said. "I will sign no death sentence at all because as a social democrat, I'm against the death penalty."
Aziz, an Iraqi Christian who majored in English literature, is 74 years old and reportedly suffering from ill health.
As foreign minister he was a familiar face on the international scene during the 1980s and 1990s.
Both the Vatican and Russia have urged Iraq not to execute Aziz on humanitarian grounds.