Sportsnet's Elliotte Friedman said Saturday that Bennett's agent, Darren Ferris, told him his client would like the team to consider giving him a change of scenery.
But the Flames were stunned by Ferris' proclamation that the forward wants to be dealt, multiple sources told Sportsnet's Eric Francis.
No one within the Flames organization is questioning Friedman's reporting, according to Francis, but he adds neither Bennett nor Ferris has communicated to the team a desire for a trade.
"One thing I've gleaned in just calling around is that (the Flames are) not in any hurry to do it," Friedman said Saturday.
Bennett, 24, has excelled in the playoffs but struggled during the regular season through his six-plus campaigns with Calgary. The Flames drafted him fourth overall in 2014.
It was also reported Saturday that another Ferris client, Montreal Canadiens defenseman Victor Mete, had "officially" asked for a trade. Canadiens general manager Marc Bergevin denied that report and said the team wouldn't be trading Mete.