Chairman Levy believes Kane can win a trophy at Tottenham
The England captain has scored 23 Premier League goals this season - behind only Manchester City's Erling Haaland - but is approaching the final 12 months of his contract at managerless Spurs.
The 29-year-old forward, who has been linked with a move to Manchester United or Paris Saint-Germain at the end of the season, has spent his whole senior career at Tottenham but is yet to win a trophy.
Spurs' record goalscorer has often made clear his desire to win silverware at his boyhood club but discussions over a new deal are yet to take place.
Levy said during a discussion at the Cambridge Union Society: "He (Kane) can absolutely win a trophy at Spurs, but being a legend is also important.
"The fact that he's the top scorer for Tottenham Hotspur, he's making history. I hope one day there is a statue of Harry Kane outside our stadium."
Long-serving chairman Levy is known for his reluctance to take part in media activities and has rarely given interviews during his 22 years at Spurs since ENIC bought the club.
The Tottenham fan reflected on a number of issues during the event in Cambridge last month, including the club's trophy drought, which has now extended into a 15th consecutive campaign.
"It has been an incredible journey and in the 22 years, Tottenham has progressed enormously," Levy said. "Not as much as a fan we would hope but hopefully the journey is not over and we are still hoping we will get that trophy that we need.
"When we first came in to Tottenham, winning was making sure we stayed in the Premier League. Then as time goes on and we get more successful, it was about getting into the Europa League and then the Champions League.
"Obviously the ultimate goal is to win the trophies. That is clearly what we are trying to do. It's easier said than done."
In recent months there has been speculation over the long-term ownership of Tottenham, with talk of outside investment and prospective buyers preparing bids for the club.
Fans have also shouted "Levy Out" at recent games.
But Levy said: "ENIC owns approximately 87 percent of the club. We have 30,000 shareholders and most of them are fans who own the shares.
"We have a duty to consider any proposal anyone wants to make. All I would say is we are not in negotiations with anybody. Nor have we been in recent months."
