"I'll tell you again, this is what I think, and it's just what I think," Babcock said. " [General manager] Kyle [Dubas] and I talk about this every day so I'm up to date on what's going on. There's lots of opinion out there. Let's not confuse opinion and facts; we think Willy is going to be here. We think Willy is going to be here for a long time. We think he's going to be a career Leaf. That's what we think, that's what we believe."
Nylander, a restricted free agent, must sign by Saturday at 5 p.m. ET to be eligible to play this season.
The 22-year-old forward, who had 61 points in each of the past two NHL seasons, has been working out with Swedish Hockey League club AIK since September, AIK sports director Anders Gozzi told Sweden's TV4 recently.
Babcock has been steadfast in his recent comments that he believes Nylander will sign with the Maple Leafs.
"I mean, Willy loves hockey," Babcock said last week. "I know Willy good. He's a great teammate and a good person, and he loves hockey. He wants to play hockey."
Forward Auston Matthews said Thursday that he hopes his former linemate will be back soon.
"I think we're just going to let that work out itself," Matthews said. "That's obviously out of our control. "We obviously want him here and we hope to have him here as soon as possible. But the clock is kind of ticking, but we really hope to have him because he's a big part of this team."
Matthews had missed 14 games with a left shoulder injury before returning with two goals and an assist in a 5-3 victory against the San Jose Sharks at Scotiabank Arena on Wednesday.
Toronto (18-8-0) is second in the Atlantic Division; they have 36 points, tied with the Buffalo Sabres, but the Maple Leafs have played one more game (26-25).
Matthews said he has been in contact with Nylander since the season began but that they have avoided the topic of Nylander's contract.
"I've talked to him a couple times but I don't really bother him with that stuff just because I can imagine what he's going through," said Matthews, who can become a restricted free agent July 1. "You know he wants to be here, he wants to play hockey. That's the main thing.
"All of us really hope this gets resolved so we don't get asked this every single day in the media and we can just go out and focus on the things that help this team. But like I said, he's a big part of this team. You know he wants to be here and I think everybody expects he'll be there very soon."
Babcock said if Nylander does sign, he does not anticipate taking long to get Nylander into the lineup.
The Maple Leafs start a two-game road trip against the Minnesota Wild at Xcel Energy Center on Saturday, (7 p.m. ET; CBC, SN1, FS-N+, NHL.TV), then play the Sabres at KeyBank Center on Tuesday.
"Willy's a good player, he's in great shape, he's got great edges and can skate," Babcock said Wednesday. "I've got no reason to think anything, but I just believe Willy likes it here, we love him here and he's a big part of it. We think he'll be back and we think he'll be up and running in a couple weeks, but we're going to play him when he gets back."
Despite Nylander's absence, the Maple Leafs are third in the NHL with an average of 3.58 goals per game, behind the Colorado Avalanche (3.80) and the Tampa Bay Lightning (3.68).
Forward Mitchell Marner said he believes Nylander will make Toronto's offense even more powerful.
"When he does get back here it's going to add more depth to our lineup and make us even deadlier," Marner said.
