But the new Maple Leaf Sports & Entertainment president and CEO is also not backing down on the concept of focusing on the present rather than the past.
"I'm not here to stomp on the alumni," he said in an interview Monday. "One of the reasons anyone wants to come and be a part of this organization is the history and tradition of the Maple Leafs.
"It is 100 years that is unbelievable and, quite frankly with the exception of maybe the Canadiens, unmatched.
"And so this is not a debate nor is it meant in any way to criticize or minimize our history. It was never meant to do that. And for that I'm extremely apologetic, because I don't want the alumni thinking there was any debate there.
"It was just a simple concept, which is at some point or another this team in its current form and fashion has to create its own legacy. And we need not to hide behind other things. That's all.
"It was a simple notion of — and it still will be and I'm not going to back away from the notion — we want to put the pressure on these guys. I want it to be about them.
"I understand our history and I honour our history and I'm proud to be a part of it now. But I also understand that at some point or another, we've got to go win another Cup. And I think the way we're going to do that is build an organization that dreams about that each and every day. That's all. It's just that simple.
"I think we could use our history and our tradition to build a legacy. But I think at the end of the day if we want to win a Cup, what we're going to have to do is we're going to have to find a team that wants to be the guys in those pictures as we walk down the hallway.
"That's all that was meant to do. And if I said it in an improper way or did something to offend people, I absolutely apologize. That's not what I'm trying to do."
Leiweke's words sparked debate among sports fans in Toronto, which has not celebrated a Stanley Cup championship since 1967. Some agreed with him, while others thought he was being disrespectful to the past.
Leiweke also turned heads when he said in earlier interviews that he had already planned a Stanley Cup parade route.
"I'm not going to back away from the parade," he said. "I probably will keep my dreams to myself for a while but it is important for this organization to have a dream. And we have to think about the uniqueness of what would happen here if we won — on all of our teams.
"And I want us to think about it. I'll probably think about it a little more quietly, that's all."
Leiweke admitted it was a change coming from a one-newspaper town in Los Angeles to Toronto, which has four dailies. But he had no complaints about recent headlines.
"We dig our own ditches," he said. "So I've dug my own ditch here."