As a young boy, a pint-sized Koivu often visited to see his older brother Saku play for the Canadiens.
"Everything was new to me as a young kid, coming to see an NHL game and seeing NHL players — (Mark) Recchi and all those players," Mikko Koivu said Tuesday ahead of the Wild's game against the Canadiens. "It was a fun time.
"I spent a lot of time here. I know my way around, but it's been a long time since I've been here. It was a great time for the whole family. It was great for a kid growing up. Hockey here in Montreal, there's not a better place to see that and to learn.
"Being able to follow him that closely was something special and I'll always remember that."
The now six-foot-three Koivu returned as captain of one of the NHL's hottest clubs. The Wild were riding a an eight-game points streak (7-0-1) after a win over Winnipeg on Sunday gave them a sweep of a three game homestand.
The 30-year-old Koivu doesn't like to compare himself to his brother, who is eight years older but is still playing in the NHL, now with the Anaheim Ducks.
Both came from the TPS Turkku club, where their father Jukka Koivu was coach.
The five-foot-10 Saku was drafted 21st overall by Montreal in 1993 and became one of the city's most popular players, although he endured a horrific run of setbacks, including major injuries to both knees, almost losing an eye to a high stick, and a battle with cancer.
Saku Koivu served 10 years as the Canadiens captain, starting in 1999 until he left as a free agent in 2009 to play with his Finnish national team linemate Teemu Selanne in Anaheim.
He joined the club in 1995, two years after the Canadiens' record 24th and last Stanley Cup conquest, and lived through some lean years, including three straight seasons out of the playoffs from 1999 to 2001.
Mikko Koivu was picked sixth over by the Wild in 2001 and was named captain in 2009.
He also endured some short seasons.
Minnesota joined the NHL as an expansion team in 2000 and made the playoffs only three times in its first 11 years before emerging as a contender last season. The big jump came when they handed big-money, long-term contracts to free agents Ryan Suter and Zach Parise and traded for former Buffalo captain Jason Pominville.
"We all know what kind of players they are on the ice, but off the ice, just with leadership and being a day-to-day example for the younger guys, it's very important," said Koivu. "You see that more and more.
"Last year was a short year and you're seeing it more this year. They're more comfortable around the team."
Saku Koivu is also on a contender now as the Ducks lead the Pacific Division.
Finnish coach Erkka Westerlund said this week that one of the Koivus, either Saku or Mikko, will be captain at the 2014 Winter Olympics in Sochi, Russia.
Saku hopes to play in a fifth Olympics after winning bronze in 1994 in Lillehammar and Salt Lake City in 2002, silver in 2006 at Turin, Italy, and bronze in 2010 in Vancouver.
Mikko also played on the 2006 and 2010 teams.
"It was a great experience, especially the first one for me," said Mikko. "I was probably the youngest guy on the team and getting a chance to play with all of them — Teemu, Teppo (Nummenin), my brother — was a great feeing.
"Now it's a bit different being in the league myself for a couple of years and in a little different role. But if you get a chance to play with your brother, it's always something special. That would be the last one for us together, pretty much. It would be a lot of fun."
Each of the Koivus also has an IIHF world championship gold medal, Saku in 1995 and Mikko in 2011. They won silver together at the 2004 World Cup of Hockey.
It seems that at every major international event, people are surprised when Finland gets to semifinals or final, but they do it consistently, on NHL rinks or on the larger international ice surfaces.
They have some NHL stars, but not as many the teams they often beat. Always having first-rate goaltending helps and they'll certainly have that again in Sochi with Pekka Rinne, Antti Niemi and others.
"The expectations are pretty much the same as they've always been," said Koivu. "There are a couple of big countries that are always the favourites, but we know we always have a chance and we showed that in the past.
"I don't think that's different than what you'll see in Sochi. There are always such good teams out there, but in the playoff rounds, anything can happen. I think we've been fortunate to play good at those moments and to be in the medal rounds. It gives you confidence for the future as well."
Another who could make the Finnish squad is Wild forward Mikael Granlund, a 2010 first-round pick.
"It's just teamwork," Granlund said the Finnish success. "Everybody knows what they're doing on the ice and they do everything they can to win. We might not have the best individuals or the best skills, but we play together. That's the biggest thing for us. We need to hold on to that."