While Armstrong doubts Tarasenko will reach an agreement with the team before the start of free agency, re-signing the Russian scoring phenom is at the top of St. Louis' offseason priorities.
"We're having conversations, but I think both sides think it's best to keep it quiet," Armstrong told Jeremy P. Rutherford of the St. Louis Post-Dispatch. "I've been clear that he's a priority for us and he understands that. Now we've just got to see if we can get a deal done."
Armstrong doesn't think other teams will try signing Tarasenko to an offer sheet because the Blues have enough cap space to match any offer.
"We're not getting active in the other markets until we know what those costs are going to be," he said. "I don't expect (an offer sheet), but if we get one, I'm comfortable that he'll be a Blue."
Tarasenko is the biggest name on St. Louis' list of restricted free agents, but the team is also working on deals with goaltender Jake Allen and defenseman Robert Bortuzzo after forward Cody Beach re-signed on Tuesday.