"Alex is a player we've scouted and watched. … We'll continue to pursue him as best we can," Dubas said of the Kontinental Hockey League forward.
Barabanov scored 137 points (62 goals, 75 assists) in 262 KHL games for SKA St. Petersburg. The 25-year-old scored 20 points (11 goals, nine assists) in 43 games this season and is a free agent.
TSN reported that Barabanov's agent, Dan Milstein, was to begin interviewing interested NHL teams Tuesday. The report said the Maple Leafs and Arizona Coyotes have been interested in the forward for almost two years and are the front-runners.
Dubas said Barabanov (5-foot-10, 191 pounds) makes up for his lack of size in other ways.
"He's a winger, he's strong, he's not tall but a very strong player," Dubas said. "[He has] great playmaking ability [and is] very good in tight.
"One of the other things we like about him is his ability to make plays under pressure. His ability to win pucks, protect pucks when people come after him and use his strength to be able to do that. A playmaking winger who can also produce at the net."
Another player who could help the Maple Leafs as early as next season is forward Nicholas Robertson, who was selected by Toronto in the second round (No. 53) of the 2019 NHL Draft. Like Barabanov, Robertson is not big (5-foot-9, 164 pounds) but is a skilled scorer.
Playing with Peterborough, Robertson was leading the Ontario Hockey League with 55 goals in 46 games when the league stopped play March 18 because of the coronavirus pandemic. He scored five points (two goals, three assists) to help Canada win the IIHF World Junior Championship.
"He's one of the more focused and hard-working [players] I've seen in my time in hockey," Dubas said. "… Come training camp we'll give him every opportunity to make the team and put the ball in his court."
As for when training camp will be, or when the 2019-20 NHL season might resume after it was paused March 12, Dubas said, "There are much more important things happening in the world right now. We try to map out as many of the situations as possible without trying to get too far ahead."
Dubas said he and his staff are concentrating on maintaining correspondence with the NHL and his superiors with Maple Leaf Sports and Entertainment. Dubas said he supports NHL Commissioner's Gary Bettman's stance that the integrity of the Stanley Cup Playoffs cannot be compromised just to declare a winner if and when the season resumes, whether an abbreviated format is adopted or not.
"I have no idea what it would look like or how it would unfold," he said. "I think these are unprecedented times and the League is looking at everything. … For me to guess would be a little bit reckless. It's not at the front of my mind and probably not the League's either."
Dubas said no discussions have been held with the NHL regarding contingency plans to finish the season. Safety has been the NHL's priority, he said.
"I know dealing with the NHL has been a great enlightenment for me and many others to see how they operate daily," Dubas said. "The way Commissioner Bettman and (Deputy Commissioner) Bill Daly and the rest of the staff there have handled this has been really enlightening for me, and for us to know that their primary concern has been the health and safety of everyone."