Spurs are on a four-match winless run in the Premier League and, as a result, Villas-Boas is the bookmakers' favourite to be the next top-flight boss to leave his post.
In an article published by One World Sports, author Duncan Castles claims that club sources have informed him that Tottenham chairman Daniel Levy and principal owner Joe Lewis are "dissatisfied" with the team's start to the season.
Castles, who has previously written for The Sunday Times and Sports Illustrated, adds that Hoddle's name was mentioned when Levy asked advisers who would be a good candidate to replace Villas-Boas.
Hoddle was a great success during 12 seasons as a player at White Hart Lane, winning the UEFA Cup in 1984, the Charity Shield in 1981 and the FA Cup in 1981 and 1982.
However, the 56-year-old was unable to continue that success after becoming the club's manager in April 2001. He was sacked in September 2003 following 104 games in charge.
Hoddle guided Spurs to 41 wins, 18 draws and 45 defeats. Villas-Boas has also masterminded 41 wins for Spurs, but the Portuguese has been in charge for just 76 matches, 15 of which have been defeats.