The Ligue 1 champions were without a manager by the end of June following the Italian's departure to Real Madrid and Villas-Boas, who is in regular contact with the French club's president, admits he was informally targeted for the vacancy.
"I have good relations with Nasser [Al-Khelaifi], with whom I speak regularly," Villas-Boas told L'Equipe.
|25/1||Tottenham are 25/1 with William Hill to beat Chelsea 3-0 on Saturday
"That PSG had approached me was released [to the press] but I wanted to stay a second year at Tottenham, building on the work of last season, making two consecutive seasons in the same club for the first time in my career.
"There has never been a written bid from Paris. We never got to that stage."
When asked if he was flattered by the interest from PSG, Villas-Boas replied: "Yes. If other people like the way you train, it's flattering, but Tottenham is a great club."
Villas-Boas also believes that Gareth Bale, who joined Real Madrid in a world-record €100 million deal in the summer transfer window, has the potential to be as good as Cristiano Ronaldo.
"With the departure of Gareth, players take on more responsibilities. They know that if they are good, we will talk more of them, so they have good reason to shine. We score a lot of goals, players who enter are good, we play more as a team," Villas-Boas said.
"Gareth Bale can have the same influence that Cristiano Ronaldo to Real Madrid because he has the potential to do so that will depend on how it fits. But at Real, he will not be the star, as he was here."