The underachieving franchise finished 17th in the 19-team league with a 6-17-11 record this season.
"Our soccer team is absolutely in complete disarray," said Leiweke, drawing laughs during an Empire Club luncheon speech about the future of MLSE teams and plans to improve them.
But the Maple Leafs Sports and Entertainment boss said change is coming.
"The team we turn the quickest will be TFC and we'll turn them next year," he said.
"Mark it down, write it down, film it .... We're going to turn TFC around and we're going to make the playoffs next year. We know where we're headed, we know how to get there. We've been given the resources of this ownership group and we will get to the right place."
Leiweke, who brought David Beckham to the Los Angeles Galaxy, says he knows how to work the designated player rules in the league.
The soccer team has money to add designated players and still have about a third of its salary cap to sign two or three veteran MLS players.
In detailing the MLSE clubs and their chances of success, he pointed to the hockey club first.
"The Leafs are close," he said.
Like the New York Yankees are to baseball and the Dallas Cowboys to football, the Leafs must become "the greatest hockey team in the history of the National Hockey League."
"Toronto is the heart and soul of the great game of hockey," he said.
Leiweke made headlines after taking over in July when he said he already had a championship parade route in his mind for the Leafs.
He did not back down from that Tuesday.
"I could not be more excited about the parade route and we're going to throw you one, I promise," he said.
Championships, he said are "not an unreasonable expectation," at MLSE.
Leiweke ruffled feathers early in his tenure when he suggested some of the photos of past Leafs greats should be taken down at the Air Canada Centre.
"No disrespect to the history and tradition of the 100 years of the Toronto Maple Leafs or any of the great players that have put on that jersey," he said Tuesday. "But these players know it's now time to put their pictures up on the wall. It's time for us to hang Stanley Cup banners."
As for the Raptors, he said it was tough to build an NBA team on the fly because of salary cap restrictions.
Luck and skill are needed in drafting players, plus intelligence in signing other players.
"To be honest with you, we haven't done that here. And I'm not blaming anybody. Now the blame's on us."
He dismissed the belief that NBA players don't want to come to Toronto. And he said the current roster is "ticked off" that some pundits are already writing them off.
"They're out to prove something this year," he said of the Raptors, who open their season Wednesday.
Build a winning culture and players will come to Toronto, he added.
On other matters, Leiweke said:
— The chances of an NFL team coming to Toronto in the next decade are "pretty good."
— Given 17 of 19 Toronto FC games were played in rain at BMO Field this season, "we've got to put an end to that, it's time to put a roof on BMO Field."
— At the requests of the city of Toronto, which owns BMO Field, MLSE is looking at whether the venue can be changed to accommodate the CFL. "The Argos are part of a conversation, not a decision that's been made."
— MLSE is looking at whether a larger block of tickets should be freed up to get some new Leafs fans in the ACC to make the venue livelier.
— The NHL needs to put hockey in the Seattle-Portland marketplace, as well as returning a team in Quebec. And that such expansion — as well as possibly in Las Vegas and Kansas City — is needed to grow the sport before talk of a second franchise in the Toronto area.Suggest a correction