Fabianus Tibo, Dominggus da Silva and Marinus Riwu were found guilty in 2001 following months of violence on Sulawesi Island between Muslim and Christian mobs that left dead around 1,000 people from both faiths.
Tibo's son, Robertus, said prosecutors had informed him by letter that his father and the two others would be killed in the early hours of Saturday morning by firing squad.
"I was very shocked to read the letter saying that my father and his friends are scheduled to be executed this weekend," Robertus said in the Sulawesi town of Tentena.
"My father is convinced that he is innocent."
All three have said they are not guilty, but their final appeal was turned down by Susilo Bambang Yudhoyono, the Indonesian president, last year.
A lawyer for the men was quoted in the Koran Tempo daily newspaper as saying that he was trying to win them a stay of execution based on new evidence.
Several hardline Muslim leaders in Sulawesi have called on the men to be executed.
Amnesty International, which opposes death sentences, said it was concerned by reports the trial of the three men did not meet international standards of fairness.