Spurs have grown into one of the Premier League's top sides under Pochettino's leadership, but have still yet to win a trophy since 2008.
Despite those setbacks, Pochettino insists the club are heading in the right direction and that their new stadium will help them push on to a higher level.
"Do I see a point where Tottenham are at the same level as Real? In the future — of course,” Pochettino said. “I believe Tottenham is going to have all the infrastructure to one day maybe be at the same level.
"It’s all about believing and building your history.
“It’s difficult, but that’s normal when you want to compete with these big sides. But I think Tottenham is going to have the infrastructure to one day be a club that can be a contender for every single title.”
Whether Pochettino will lead Spurs forward is one of the club's biggest questions, as the Argentinean continues to be linked with the managerial positions at Manchester United and Real Madrid.
The 46-year-old was again quizzed about his future on Tuesday, and he refused to commit to Tottenham in the long term.
"I can’t promise that,” Pochettino said.
“Look, it depends on the mood of my chairman, depends on the decision of the company. It’s not only my decision to be here.
"When I signed the contract a year ago, I signed for five years. I am here and respecting my contract, of course, but in football to sign a five-year contract doesn’t mean you’ll be here forever — like the players, like every employee of the club.”
Spurs, who are currently third in the Premier League table, will take on Watford at Wembley Stadium on Tuesday.