"When's he's ready to play, he'll let us know he's ready to play," Canucks coach Alain Vigneault said Friday, a day after Sundin agreed to a one-year deal.
The 37-year-old former Toronto Maple Leafs captain is expected to arrive in Vancouver on Dec. 27. He has been skating with a professional team in Sweden, and could be ready to play early next month.
"I know it's not a perfect situation as a player," Sundin said on a conference call. "The players are in midseason form and it's going to be challenging. The next few weeks I am going to push myself to make sure I'm in the best shape I can be in. I'm happy there was no player movement because I was joining the team."
Entering play Friday night, the Canucks were tied with the Calgary Flames for first place in the Northwest Division with an 18-11-3 record.
"To pick a team that is going to win the Stanley Cup is impossible," Sundin said. "The league is too competitive. I do know Vancouver has a good enough team to compete for the Stanley Cup. I'm thrilled to be part of that team.
"Once you get to (the playoffs) who knows what is going to happen? I'm thrilled about getting the chance to play."
Star goalie Roberto Luongo, still recovering from a groin injury, said Sundin presents a big presence on the ice that demands attention from the other team.
"We're all excited to have him," Luongo said. "We're not going to be expecting him to save the world. We know we have to keep doing our job and working hard."
Center Henrik Sedin grew up in Sweden idolizing Sundin.
"He's a guy we looked up to when we were growing up," Sedin said. "He's big, he's strong, he's great at faceoffs. He brings everything to our team. He's going to make a lot of players better for sure."
Sundin scored 32 goals last season for Toronto, and has 555 goals and 766 assists in 17 seasons with the Quebec Nordiques and Maple Leafs.
"If I didn't play this year, it would have been really hard for me to compete anymore at the highest level of hockey," Sundin said. "I think that made me decide I wanted to give it another chance to play in the NHL."
Sundin talked to Canucks defenseman Mattias Ohlund to see if his signing would disrupt the Vancouver locker room.
"I just wanted to get a feel about how the team felt about adding another player midseason," Sundin said. "I've been on teams and any time there are changes ... I think those are things that affect what goes on in the dressing room."
Mike Brown, who had been wearing Sundin's usual No. 13, already had switched to No. 15 for practice Friday.
"Mats is incredible," said Wellwood, who teamed with Sundin in Toronto. "He's just like Luongo. There are some games he takes it over. For him to come and fit in on the team, there is no concern."