"Those reports are unfounded and not true," Benning told the radio station. "I don't know where that came from. We are in constant contact with his group.
"Contract talks have gone in the right direction. We want to get him signed."
Sportsnet had reported May 30 that contract negotiations between the 22-year-old and the Canucks were "not close at all."
The No. 23 pick in the 2015 NHL Draft, Boeser can become an RFA on July 1 after completing the three-year, entry-level contract he signed March 25, 2017.
Boeser was third on Vancouver in scoring this season with an NHL career-high 56 points (26 goals, 30 assists) in 69 games. He has 116 points (59 goals, 57 assists) in 140 games during three seasons with the Canucks.
In his rookie season in 2017-18, Boeser had 55 points (29 goals, 26 assists) in 62 games and finished second to New York Islanders center Mathew Barzal in balloting for the Calder Trophy, awarded to the NHL rookie of the year. Boeser was named most valuable player at the 2018 NHL All-Star Game when he had three points (two goals, one assist).
Vancouver also would like to sign defenseman Alexander Edler, who can become an unrestricted free agent July 1, Benning said. The 33-year-old has played his entire 13-seaon NHL career with the Canucks, who selected him in the third round (No. 91) of the 2004 NHL Draft.
"We are going to keep talking with Edler's agent," Benning said. "Sometimes the different sides have different things they are trying to accomplish. We have not found common ground yet. We want Alex back and will try and figure it out."
Edler, who missed 26 games this season because of injuries, led Canucks defensemen with 34 points (10 goals, 24 assists) in 56 games.
In 814 NHL games, Edler has 368 points (94 goals, 274 assists).