The Lilywhites have mounted a push for the Premier League title, and they are currently just five points behind Leicester City.
Schmeichel feels that it is now a two-horse race to win England’s top flight, and the Manchester United legend has predicted that Spurs will have a very bright future.
"Spurs have been fantastic,” the Dane said. “They've played some very entertaining football, they've got great players, great individuals and they are going to push and push and it's looks like they are ready to take the challenge on, even in the longer run as well.
"It's a race between Spurs and Leicester. We will get, I think, a new Premier League champion.”
Tottenham have surpassed all expectations this season, to start challenging for the title.
Mauricio Pochettino’s side were considered top four candidates before the campaign progressed, but they have shown brilliant form to challenge Leicester.
While the Foxes have been relentless this season, Spurs have just about kept pace with Claudio Ranieri’s men.
Tottenham now have their best chance ever to win the Premier League title, but they face a tough test at the weekend.
Spurs are set to travel to Anfield on Saturday evening, and if they are able to pick up a victory it would reduce the gap at the top of the table to just two points.