1997 world champion Villeneuve, who drove for the British team when he won his title over 20 years ago, is a serial critic of his fellow Canadian Stroll.
"They already sold their soul to the billions of Lawrence Stroll, who only cares about his son," Villeneuve said.
Stroll, 19, hit back in the pages of the French publication Auto Hebdo: "I don't pay too much attention to what he's saying.
"It's always going to be negative anyway. He never supported me, in every sense of the word. He only sees the negative. Even the Baku podium was not a positive in his eyes."
Williams's 2018 lineup - expected to be made official in the next week or so - is raising eyebrows throughout the motor racing world, but two-time champion Mika Hakkinen says that sponsorship is just part of the puzzle as a driver moves towards F1.
"You definitely need all the elements to get into Formula 1 - [including] good contacts and a lot of money," he told Sonntagszeitung.
"It's difficult to name an exact number, but when you reach Formula 1, you've already burned millions."
The 2018 world championship gets underway win March.