The goalie can become an unrestricted free agent July 1.
"We've started the process of moving things around," Weisbrod said. "There have been some sort of good place-setting conversations to sort of get a handle on what we're looking at and what's the best interest to him and what's the best interest to the team, and obviously I'm hopeful that somewhere down the stretch here we'll be able to find some middle ground and get it worked out."
Markstrom, who turns 30 on Jan. 31, is 18-13-3 with a 2.71 goals-against average and .916 save percentage in 34 games this season. He is in the final season of a three-year contract and will represent the Pacific Division in the 2020 Honda NHL All-Star Game.
The Canucks (27-18-4), who have won four of their past five games and are in first place in the division, next play the St. Louis Blues on Jan. 27 following their League-mandated five-day break.
"We know that we want him back, we know that he wants to be here," Weisbrod said. "We don't want it to get too in-depth during the season because we want his head focused on the games and what we need to do as a team and being able to focus on things on the ice down the stretch."
Markstrom has played 60 games in consecutive seasons with the Canucks and is 94-90-26 with a 2.73 GAA and .912 save percentage in 220 games (209 starts) for Vancouver since he was acquired in a trade from the Florida Panthers for goalie Roberto Luongo on March 4, 2014.
"He's obviously been a very important part of our group," Weisbrod said. "Whether it works itself out while we're still playing or whether it becomes a summertime issue, I don't think that's of great concern. … Obviously, once you start conversations it's going to move at the pace that it moves. We do have what we consider a long runway in terms of time to get it done."
