This week's two preseason games between KHL and NHL clubs, beginning with Monday's game between St. Petersburg SKA and the Carolina Hurricanes, is just the beginning, Medvedev, president of the KHL, hopes.
"With these games this week, we wanted to bring back the flavor of Soviet and NHL teams playing," Medvedev told ESPN.com on Monday over the phone from St. Petersburg. "I think the fans around the globe will appreciate that it happened, and I really hope that we'll find a way to continue to have such types of competitions."
The Phoenix Coyotes also play an exhibition game Wednesday in Latvia against KHL club Dinamo Riga. The Coyotes open their regular season against the Boston Bruins in Prague this week as part of the NHL's six-team, 12-game Premiere Games event. The Hurricanes play the Minnesota Wild in Helsinki, while the San Jose Sharks and Columbus Blue Jackets open their 2010-11 campaign in Stockholm.
The question is, will the NHL's Premiere Games ever go to Russia?
"We're hoping for that idea," Medvedev said. "It would have interest from the public, especially if you combine with [preseason] games between KHL and NHL teams. ... I think it would be a great idea to bring those teams that have Russian players like Washington with Ovechkin and Pittsburgh with Malkin. I'm 100 percent sure it would be sold out."
Medvedev, who doubles as the board chairman for SKA St. Petersburg, a club that features Alexei Yashin, Denis Grebeshkov, Sergei Zubov and Evgeni Nabokov, also sees the potential in having KHL clubs tour the NHL across the pond, reviving the old Summit Series tours of the 1970s and '80s.
"Yes, it should be a two-way street, it shouldn't just be in Russia. We should bring some KHL clubs to North America," Medvedev said.
The KHL and NHL have come a long way in just a few years. When Medvedev established his new league with the inaugural 2008-09 season, with his league poaching Alexander Radulov from the Nashville Predators in the process, the NHL and KHL were at each other's throats.
But calmer heads have prevailed, helped in large part by meetings in Vancouver this past February during the 2010 Winter Olympics. Medvedev said he's also just agreed to a deal with NHL deputy commissioner Bill Daly regarding player contracts.
"The day before yesterday, Bill Daly and I reached a formal agreement about the appreciation and respect of the KHL contracts," Medvedev told ESPN.com. "It's very important. We have a legally binding agreement. This agreement confirms the validity of KHL contracts and is fully in compliance with hockey industry standards."
Daly confirmed the agreement in an e-mail to ESPN.com on Monday.
"I sent him a letter confirming that we recognize and respect the validity of the standard terms of KHL SPCs," Daly wrote. "But that's always been our position -- this doesn't represent a change for us.''
The apparent détente between the NHL and KHL cannot be understated. The two leagues must learn to co-exist if the NHL sends its players to Sochi, Russia, for the 2014 Games. But that's a story for another day.