The Dutch international, who arrived in north London from Real Madrid on transfer deadline day, has proved himself as one of the signings of the summer, notching five goals for Spurs already this season.
Attacking midfielder Van der Vaart is keen to continue his good form at Tottenham, and feels silverware is not out of the question for Harry Redknapp's side.
"When you see the squad, nobody wants to leave and that's saying a lot about this club," Van der Vaart told the Daily Star.
"I want to stay at Tottenham. I'm here for the long run.
"I want to make this a really big club and I hope I can win something. I think it's possible - that's why I'm here."
Spurs, who made their Champions League debut this term, currently sit fifth in the Premier League standings after nine games.
And 27-year-old Van der Vaart insists a second consecutive top-four finish is on the cards this term.
"I have a lot of confidence that we are going to be in the Champions League again next season," he said.
"The pressure is really high, especially when you play in the Champions League and then a few days later in the league.
"It's really difficult to win every game, but I think until now we are doing a great job."
Van der Vaart also feels Spurs are close to becoming serious league title contenders, adding: "It's a little step but it's still a step. I think within a few years it's possible, because everything is possible."
Spurs travel to Manchester United on Saturday tea-time unbeaten in three league games, and Van der Vaart is looking forward to taking on the top flight giants.
"I love to play in big games," he added. "That's always a dream for a player to play a great match."