McKenzie tweeted that the Flames are "believed to be working towards new contract for Russell."
While the deal is "not done yet," McKenzie indicated that it's "heading in that direction."
Russell, 26, has picked up four goals and 15 assists for 19 points in 41 games with the Flames so far this season.
Flames President of Hockey Operations Brian Burke has started to retool his roster, as he searches for a new GM.
Last month, the Flames signed center Matt Stajan to an extension, and re-signing Russell would be another step in stabilizing the club's roster.
With Russell inching closer to his new contract, two other members of the Flames could be inching closer to a ticket out of town.
Forwards Mike Cammalleri and Lee Stempniak, both pending unrestricted free agents, have attracted a lot of interest from other teams and are expected to be moved by the March 5 trade deadline.
The Flames recently opened contract talks with Cammalleri, though it's believed he will test the free agent waters this summer.
Cammalleri also owns a limited no-trade clause and can list up to seven teams he won't accept a move to. That list was submitted in the off-season, though it's unclear if it's been recently revised.