The Portugese coach is odds-on favourite with SkyBet after significant backing on Thursday evening, with White Hart Lane chiefs understood to have made initial contact.
Villas-Boas was sacked by Chelsea in February but is thought to be keen on a return to London.
Everton manager David Moyes and Wigan’s Roberto Martinez are both strong candidates to replace Redknapp, who was sacked on Wednesday night, but both would bring compensation costs.
Latics chairman Dave Whelan has already said he will not stand in Martinez’s way, should Spurs make an approach.
“If Tottenham come to me and ask to speak to him, I have to say the answer is ‘yes’. It always is,” Whelan said.
“You cannot stop managers moving. Every club that people regard as a big club, when these jobs come up, people say ‘oh Roberto must be in for that’.
“But I have not heard one thing from Tottenham Hotspur or from Roberto, so as far as I am concerned there is nothing going on at present.”