Another of Mr Aziz's co-accused is Saddam Hussein's half-brother, Watban Ibrahim al-Hassan.
The executed merchants had been accused of hiking food prices at a time when Iraq was under international sanctions.
Mr Aziz's son, Ziyad, has insisted that his father is innocent in an interview with the BBC.
"He sent me a message through a lawyer saying, don't worry about me, I am strong," Ziyad Aziz said.
"Everybody knows that he was not involved in this thing, but the Iraqi government has accused him and [plans to] put him on trial because of his name, because he is Tariq Aziz.
"Even though he was part of the regime, everybody knows my father was responsible for foreign relations of Iraq and other countries… he was not involved in this thing about the merchants."
Mr Aziz received hospital treatment last year after a fall in prison, while in 2006 he suffered a stroke.
He was taken into custody in April 2003 after he gave himself up to US forces.
Tariq Aziz's son Ziyad on his father's trial
The trial is being conducted by the Iraqi High Tribunal, which was set up to try former members of Saddam Hussein's regime.
It will be conducted in a similar way to previous cases, with the court first hearing from complainants, then from witnesses, and finally from the defendants, tribunal spokesman Areef Shaheen told the BBC.
Saddam Hussein was executed in December 2006 after being convicted of crimes against humanity over the killing of 148 Shia men and boys after a 1982 assassination attempt against him.
Judge Rauf Rasheed Abdel Rahman, an Iraqi Kurd, is presiding at Mr Aziz's trial. He is the same judge who sentenced Saddam Hussein to death.
Human rights groups have criticised the Iraqi High Tribunal on a range of issues.
Human Rights Watch issued a report into the trial of Saddam Hussein which concluded that the process was flawed and its verdict unsound because of "serious administrative, procedural and substantive legal defects".
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