There has long been talk about the potential of a newly-formed league consisting of the best clubs from across the continent.
Four years ago Arsenal manager Arsene Wenger predicted such a league would become reality within a decade, although the idea has yet to get off the ground.
Galatasaray chief Aysal reignited the debate at the Leaders in Football conference on Thursday, calling for the creation of a 20-strong league.
"I think it is the future of football," he said. "It has to be created, not after 10 years but as soon as possible.
"Football is a big industry, a growing industry, and a European super league will bring a lot of support and also energise football in general.
"I think it could be 20 big teams, for example, in Europe, with the last three, four or five teams can change every year.
"I think it can be operated in a proper way in order to make it effective and useful to European football and also to bring new horizons in football."
Aysal would prefer the league to be controlled by clubs rather than UEFA, but would welcome the governing body starting the initiative.
The Turk was keen not to mention potential English involvement, but was more forthcoming when asked about interest from the Premier League in one of his players.
Burak Yilmaz has shone since joining Galatasaray two years ago, leading to reported interest from Chelsea.
When asked if he would allow the Turkey international to leave for Stamford Bridge, Aysal said: "If he wants to go and Chelsea are interested then of course, why not? I favour Turkish players going to Europe to play in European leagues.
"No [we have not received an offer from Chelsea], not yet.
"We had some requests from Lazio at the end of the summer, but the deal didn't go through because the conditions were not satisfied."
For the time being Yilmaz will no doubt play a key role as Roberto Mancini attempts to turn around Galatasaray's fortunes.
The former Manchester City boss was recently appointed manager of the Istanbul giants, penning a three-year deal to replace Fatih Terim.
Mancini secured an impressive 2-2 Champions League draw at Juventus in his first match at the helm, only to lose his first league match 2-1 at Akhisar Belediye.
That left the reigning champions 13th in the Super Lig standings but Aysal believes Mancini can help spring a revival.
"We have had high-calibre managers at Galatasaray before and at other clubs in Turkey," he said.
"I hope that Mr Mancini will do a good job at Galatasaray. I am counting on him.
"He has huge experience in the Champions League and also in the Italian and English leagues.
"I hope that he will bring new blood and new oxygen to Galatasaray."
The European Club Association responded to Aysal's comments, with chairman Karl-Heinz Rummenigge backing the current Champions League set-up.
A statement read: "The European Club Association (ECA) has taken note of comments made today regarding the alleged creation of a European Super League in 2018.
"ECA underlines that such idea was never discussed within the association and never figured on any meeting agenda. ECA is very happy with the current European club competitions."
Rummenigge said: "Our European Super League is the UEFA Champions League!
"We are very happy with the current competitions and our extremely fruitful collaboration with UEFA.
"We will continue to work together with UEFA, and this beyond 2018."