O'Reilly, the St. Louis captain the past two seasons, said he wants to remain a part of the core group. He has one year left on the seven-year contract he signed with the Buffalo Sabres on July 3, 2015.
"It's a place I want to be," O'Reilly said. "Yeah, it's crazy going into a contract year. It feels like time kind of flew by. Yeah, I'm sure things, over the summer and going into next year, I'm sure we'll try to figure something out. Again, the season just ended, so we haven't really had time to discuss it. But yeah, if it happens, it happens."
Barbashev, who had NHL career-highs in goals (26), assists (34) and points (60) this season, has one year remaining on a two-year contract and can become an unrestricted free agent after next season.
Armstrong was also asked about forward David Perron, defenseman Nick Leddy and goalie Ville Husso, who can each become an unrestricted free agent July 13.
Perron tied for third on the Blues in goals (27) and finished with 57 points in 67 regular-season games. The 34-year-old led the Blues in goals (nine) and points (13) in 12 playoff games.
"I'd love to be back," Perron said. "The desire has been there for me last year, during the year and right now. So, it's what it is.
"Just for our kids, they're in school right now and they love the city and just like we do, just like I do and obviously playing with [O'Reilly], beside me the whole group I'd love to keep going. I feel like I've built myself as a player over the years and I want to keep this going for sure."