Nylander, a 22-year-old restricted free agent, must sign by that deadline, set by the NHL/NHLPA collective bargaining agreement, to play in the NHL this season.
He can sign with the Maple Leafs, or with another team if Toronto trades him, before the deadline.
"At this point, there's really nothing we can do. If he signs, he signs, great. If not, we'll move on," Toronto defenseman Morgan Rielly said after practice in Minnesota on Friday. "Obviously, we miss Willy, but it is what it is. We'll be here tomorrow night, with or without him."
Nylander, who had 61 points in each of the past two seasons with Toronto, has been working out with AIK of the Swedish Hockey League since September, AIK sports director Anders Gozzi told TV4 in Sweden.
Toronto coach Mike Babcock has said repeatedly in the past week he believes Nylander will sign with the Maple Leafs. On Friday, Babcock said he had spoken to Nylander on a few occasions this season.
"We're not begging anyone to be a Leaf, that's not it at all," Babcock said after the outdoor practice prior to their game against the Minnesota Wild at Xcel Energy Center on Saturday (7 p.m. ET; CBC, SN1, FS-N+, NHL.TV), two hours after the Nylander deadline passes. "It's a privilege to be here for me and for anyone else."
If Nylander signs, Babcock said he believes he will be ready to play in short order.
"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."
Babcock reiterated after the morning skate Saturday that it shouldn't take long for Nylander to be ready to play,
"I'm just hopeful Willy is going to be in our starting lineup whenever he gets over here," Babcock said. "I like the player. He's a good player. The team needs him. We want him back."
Toronto (18-8-0) is second in the Atlantic Division; it has 36 points, one behind the Tampa Bay Lightning (18-7-1). Without Nylander, and with center Auston Matthews missing 14 games with a shoulder injury before returning Wednesday, the Maple Leafs were third in the NHL at 3.58 goals per game, behind the Colorado Avalanche (3.80) and Lightning (3.73).
If the deadline passes and Nylander has not signed, he would remain a restricted free agent entering this offseason, which begins July 1, 2019 and when Matthews and forward Mitch Marner also can become restricted free agents.
"I don't know if you guys (media) think that we're tracking your tweets and things, but we're not. Sorry," Rielly said. "It's not even anything that we think about. It's not even anything that we really talk about. If he's here in a few days, then great, if not, then we're in the same position we are right now and we feel pretty good about it."
NHL.com correspondent Jessi Pierce contributed to this report
