“I would not want a closed league,” Stillitano told BBC Radio Leicester.
“I would want these magical teams, like Leicester, to be a part of this.”
Leicester, who narrowly avoided relegation last season, are seven points clear of Tottenham at the top of the Premier League with six games remaining.
The Foxes need 12 points from their final six games to become champions.
“Can you imagine if they were left out of the [Champions] League after what they’ve done? It would be absurd,” continued the American. “They are maybe the [best] sports story ever.
“If they win the Premier League this year, I cannot think of any accomplishment bigger than what they’re doing.”
‘Who is more integral?’
After last month’s meeting with officials from Manchester United, Arsenal, Chelsea, Liverpool and Manchester City, Stillitano said the change to the Champions League format was “being discussed all over Europe”.
At the time, he was quoted saying: “What would Manchester United argue: did we create soccer or did Leicester create [it]?
“Let’s call it the money pot created by soccer and the fandom around the world. Who has had more of an integral role, Manchester United or Leicester?
“It’s a wonderful, wonderful story – but you could see it from Manchester United’s point of view, too.”
‘I’m no architect’
Stillitano said those comments were “unfairly treated”, and that the opinions of Juventus president Andrea Agnelli and Karl-Heinz Rummenigge, chairman of the European Clubs Association, will shape the Champions League debate.
“I was very clear that I am not the architect, I am not behind it in any way, shape or form,” Stillitano said.
“I was just commenting that different people are saying different things.
“You’ve had the real leaders of football talking about it, not me – some guy from New Jersey. All I was commenting on was that the conversation was out there, it’s not mine.
“I think, honestly, that was misquoted. When the report came out, it’s fair to say my comments were really unfairly treated.”