The Daily Star says AVB’s representatives have held talks with club officials in London since Harry Redknapp’s sacking on Thursday.
David Moyes, who has been at Everton for 10 years, was installed as the favourite to succeed Redknapp, 65.
But ex-Chelsea chief Villas-Boas, 34, is the first manager Spurs have contacted.
Villas-Boas had a torrid time at Stamford Bridge and was sacked after just nine months.
But he impressed at Porto where he won the treble in his only season with the Portuguese club.