"I think we are all hopeful, but he is going to have to get on the ice pretty soon if we are going to see him," Cooper said Sunday.
Hedman, on injured reserve, did not skate when the Lightning practiced at Hovet Arena a few hours after arriving in Sweden. But Cooper said that was the plan all along because of concerns about the seven-hour flight affecting Hedman's recovery from the lower-body injury he sustained Tuesday against the New York Rangers.
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The Sweden-born defenseman, who has nine points (two goals, seven assists) in 11 games, has not skated since and missed games against the New Jersey Devils on Wednesday and the New York Islanders on Friday.
Cooper said he would like to see Hedman take part in practice Tuesday. The team is off Wednesday and will have an open practice Thursday.
"It is what it is," Hedman said. "I'll do whatever I can in my power to be back, but I'll just focus on the process and take it day by day.
"For me, you always want to play in games, and it stinks not playing, but right now I wasn't on the ice today and we'll see tomorrow."
The Lightning and Sabres play a second game in Stockholm on Saturday (1 p.m. ET; NHLN, SN1, SUN, MSG-B, NHL.TV).
Hedman, who is from Ornskoldsvik, a coastal city approximately 330 miles north of Stockholm, is the Lightning's only Sweden-born player. He is also their de-facto tour guide for this trip.
On the bus ride from the airport to the hotel, he was pointing out various landmarks. Defenseman Kevin Shattenkirk said Hedman was almost giddy with excitement.
"It's obviously been a long day flying in from New York," Hedman said. "As soon as you saw land and you start making that approach, you feel right at home. I'm super excited to be back in Sweden and looking forward to the games."