The final decision will be made by the league in conjunction with the IIHF, but Fasel knows who he wants.
"As a Francophone who grew up as a Canadiens fan, it would be a dream for me to have the Canadiens," he said during an interview in French on Tuesday. "But the decision is not up to me. We will have to talk with the league."
The three-team series itself was unveiled officially during a news conference at the IIHF World Hockey Championship.
Fasel said the IIHF is seeking to "bridge the gap" between the North American and European hockey worlds and wants to work even more closely with the NHL.
An annual series in September between an NHL team, the European champion and at least one other European team is a start. The third team could come from the tournament's host city, which will be chosen based on a bidding process and the strength of its local club.
Fasel made it clear that the IIHF is not interested in having teams in Europe compete for the Stanley Cup, but would one day like to have the Stanley Cup champion playing the European champion.
The first event will happen in the third week of September 2008 in a yet to be announced European location. The teams will compete for the Victoria Cup, which is named after the Victoria Skating Rink in Montreal where some believe hockey was first played.
As part of plans for the IIHF's 100th anniversary in 2008, a small monument will be placed at the spot where the Victoria Skating Rink once was. It's currently a building and parking lot for a rental car company.
The IIHF will also hold its general congress in Montreal after the completion of next year's world championship in Halifax and Quebec City.
The Canadiens are the oldest professional hockey team in the world and celebrate their own centennial anniversary in 2009. They would be a perfect fit for what Fasel has in mind for the inaugural exhibition series.
"We'd like to have a team that has a great history behind it like the Original Six teams do," he said.
The IIHF expects the decision about which NHL team will play in the event to be made by December.
The first European team that competes in 2008 will be the winner of the European Champions Cup tournament next January in St. Petersburg, Russia.
The teams will be playing for a first prize of roughly C$900,000, with a total of C$15.3 million distributed throughout the tournament.
Starting in 2008-09, the IIHF has developed the format for a Champions Hockey League that will determine one of the European challengers.
Horst Lichtner, general secretary of the IIHF, hopes the new European league will help hockey teams start building brands like their soccer counterparts have.
"I think it's a great opportunity for the European clubs," said Lichtner, who was the marketing chief of the 2006 World Cup in Germany.
The North Americans could also potentially benefit from an increased presence in Europe.
Andy Murray, who coaches the NHL's St. Louis Blues, says he wouldn't be upset if the league chose his team to participate. Forward Rick Nash also wouldn't mind if the NHL picked his Columbus Blue Jackets.
"I think it would be great for marketing, for the fans . . . and to see how both leagues kind of stand up," said Nash.
The IIHF is taking an ambitious approach to its "centennial celebrations."
In addition to the September series and holding the first ever world championship in Canada, it will:
-officially recognize the 18 players who have won Olympic gold, world championship gold and the Stanley Cup. That group includes Canadians Joe Sakic, Brendan Shanahan, Rob Blake and Scott Niedermayer.
-poll 50 experts to help name a centennial all-star team.
-construct an outdoor rink at the IIHF headquarters in Zurich.
Forging stronger ties with the NHL is also a priority.
Fasel has been the IIHF president since 1994 and has seen that relationship improve dramatically. And there's still plenty of room for growth.
"We have to improve (the relationship) even more," said Fasel. "And we will. I think we have to work together to be strong together."