Spurs have not finished above their bitter rivals in the Barclays Premier League since Gerry Francis was in charge of the club in the 1994-95 season.
Since that year Arsenal have won seven major trophies and reached a Champions League final while Tottenham have struggled to keep pace with their rivals.
The last two years have seen Spurs mount something of a comeback, however.
Last season under Harry Redknapp the club held a 10-point advantage over Arsenal at the end of February until a spring collapse allowed Arsene Wenger's men to clinch third spot.
But with Arsenal currently struggling in the league, and Villas-Boas exuding confidence, the Portuguese sees no reason why this cannot be the year where the balance of power in north London finally shifts.
"We have to (finish above Arsenal)," Villas-Boas told a press conference.
"It is possible to bridge the gap.
"We are looking at trying to shorten the gap and not letting it grow.
"To play for fourth spot is difficult bearing in mind the competition you have to overcome. It's possible to bridge it.
"Arsenal have won trophies in recent times and they have qualified for the Champions League more often. That is where we want to be in the future. We're getting nearer."
Villas-Boas got his first taste of a London derby last season when his Chelsea team faced QPR and Fulham.
But the narrow gap between the two teams in terms of their league position - Spurs are one point and one position above Arsenal, who are in eighth - and the quality of their respective squads makes this a much more meaningful fixture.
Last season Spurs and Arsenal served up one of the most memorable north London derbies in history when the Gunners fell 2-0 behind at the Emirates Stadium before staging a remarkable comeback that saw them emerge with a 5-2 victory.
Villas-Boas has been left in no doubt as to the importance of the fixture.
"I have been getting it for the last two weeks, people have been speaking about it quite often - the staff, the fans and the chairman," the 35-year-old said.
"This is a game where passion is very high, it's a game that represents more than three points because of the history of north London derbies.
"The chairman keeps on mentioning it. I think it's normal.
"You really have to embrace it because it's part of the greater culture of the English game. You can't wear red at this training ground."
Some have suggested that Tottenham will have no better chance of beating their arch rivals given the Gunners' poor start to the season.
Wenger's men conceded five against Reading, lost to Norwich and scraped a draw against Fulham last week, leaving them 11 points off the top of the table.
Villas-Boas does not subscribe to the theory that Arsenal are in free fall under Wenger, however.
"Their position (in the league) is completely irrelevant," he said.
"Last season they had a poor start and managed to clinch third spot by picking up points. You drop three points, you are condemned.
"This is the nature of the Premier League."
Spurs' chances of victory took a hit today when Villas-Boas confirmed Mousa Dembele will miss Saturday's game with the niggling hip problem that has sidelined him for the last seven games.
There was more encouraging news, however, regarding Aaron Lennon, who suffered a hamstring injury in last weekend's 2-1 defeat at Manchester City.
"Lennon had a scan yesterday and his hamstring is fine," Villas-Boas said.
The Portuguese does have doubts over Kyle Walker and Jermain Defoe, who also suffered hamstring injuries against City.
"We will have to wait and see (if they recover)," he added.
"They have trained separately this week."