The former Spurs boss says the next man in charge should now challenge for the Premier League title after his signings transformed them into a 'top four' team
The 65-year-old was sacked by Spurs earlier in June after guiding the club to a fourth-placed finish and is likely to be replaced by former Chelsea boss Villas-Boas.
Redknapp says that the Portuguese manager must build on the foundations he laid at White Hart Lane and challenge for the title, if he were to get the job.
“He’s been to Chelsea and things didn’t work out, but obviously the chairman of Tottenham thinks he can do the job at Tottenham,” Redknapp told Sky Sports News.
“He has certainly got the players there to be a top four team every year and challenge for the championship."
He added: “In the last four years we came from nowhere to be a top four team and the next step is to win the championship. I don’t think that is impossible for them.”
Rumours have linked star midfielder Luka Modric with a move away from White Hart Lane this summer but Redknapp is not convinced the Croatian will definitely leave.
"I don't know. I wouldn't be sure about that," he responded when asked if Modric had played his last game for Spurs.
"It would be [a huge loss]. He is irreplaceable. But if they get massive money, they can go and get three or four players and improve the team in other areas.
"He's a great lad, comes in every day and just gets on with it. Low maintenance, loves playing football, polite, well brought up - top-class boy. As we saw in the European Championships, he can play in any team in the world - he's a different class."
The 65-year-old manager also lavished praise on Gareth Bale, who recently signed an improved deal that will keep him at White Hart Lane until at least 2016 - and said he will become one of the best players in the world.
"He is a great player. Not only is he a great player, he is a top-class boy," he said.
"He will go on and become one of the great players in world football. He is already, in my opinion. But he will be the best left-sided player, for sure."
When asked to comment on his sacking from his job with the north London club, Redknapp said there was 'no hint' that he was to be fired and spoke with fondness about his time at the helm - despite a reported falling-out with chairman Daniel Levy.
"I would obviously love to have stayed," he said.
"Things were going well. There was no hint of me leaving, to be fair.
"But it is up to the chairman and the owner. It is their club, if they feel they want to go down a different route.
"Managing Tottenham was great, I loved every minute of it. Absolutely loved it. But it's only a job."
The former West Ham and Portsmouth manager also commented on England's future, after being pipped to the managers position by Roy Hodgson.
He continued: “We’ve got good players in this country, better than we give ourselves credit for.
"It’s just about Roy [Hodgson] getting them to play the right way. Let’s be bold, let’s be positive, let’s come out and play, let’s pass the ball and if he does that we will be successful.”