The 35-year-old was sacked by Chelsea in March 2012 after less than nine months in charge of the Stamford Bridge club.
However, Villas-Boas bounced back with a return to the English top flight when he was appointed as manager at White Hart Lane to replace Harry Redknapp in July last year.
Ancelotti asked to be released from his PSG contract, which has one year to run, last month, according to a report in The Guardian.
The former AC Milan coach took PSG to their first Ligue 1 title since 1994 with the help of star players such as Zlatan Ibrahimovic and David Beckham, who joined the club in January on a short-term deal before retiring from the game at the end of the season.
However, the integral question for Tottenham supporters and the club will be how the loss of Villas-Boas would affect the future of star man Gareth Bale.
The Wales international has been strongly linked with Real Madrid, and Bernabeu president Florentino Perez has hinted that the 23-year-old would be worth breaking the world transfer record for, as Antony Kastrinakis of The Sun reported.
Bale is a big admirer of Villas-Boas' playing style at Tottenham and, in a recent interview with Spurs TV, he credited the Portuguese coach for improving his game during his season in charge at White Hart Lane, as David Kent of the Daily Mail reported.
He (Villas-Boas) has helped me in all aspects of my game.
In training we have been working on things that I can do in games and in games he has given me the confidence to do what I want and do what I do best, which is a massive thing for a player.
Bale's future remains unclear, but the loss of Villas-Boas would be an enormous blow to hopes of keeping the mercurial Welshman at Tottenham.