The 87-year-old filmmaker said he was advised by a friend to ask for the same fee as the franchise's star Arnold Schwarzenegger, and was floored when his request was granted by the production company.
"I can't be bought," Scott told The Guardian of his decision to decline, adding: "I thought: 'F*** me.' But I couldn't do it. It's not my thing."
Scott likened the task of directing Terminator 3 to directing a James Bond film: "The essence of a Bond movie is fun and camp. Terminator is pure comic strip," he said. "I would try to make it real."
He added: "That's why they've never asked me to do a Bond movie, because I would f*** it up."
Avatar director James Cameron directed The Terminator and its sequel Terminator 2: Judgement Day - widely considered one of the greatest sci-fi films ever made - before stepping away from the franchise.
Cameron's plans for Terminator 3 were scuppered shortly after the second film's release when the production company that owned half of the rights filed for bankruptcy and the rights were sold off.
The director never revealed his initial plans for the franchise's third instalment, and more than a decade passed before Jonathan Mostow replaced him to make 2003's Rise of the Machines.
Most recently, he directed The Last Duel, his 2020 adaptation of Eric Jager's book The Last Duel: A True Story of Crime, Scandal and Trial by Combat in Medieval France, starring Adam Driver, Matt Damon, Ben Affleck and Jodie Comer.
In her three star review, The Independent's Clarisse Loughrey dubbed the film "a perfectly engrossing slice of historical intrigue" that "functions as broad entertainment".