The 28-year-old defenseman has one season remaining on the five-year, $27.5 million contract ($5.5 million AAV) he signed with the Blues on July 20, 2017.
Parayko said he is intrigued with the possibility of playing his entire NHL career in St. Louis.
"For sure, that's special, that's really cool," he said. "Obviously, the first year in the NHL Draft, I didn't get drafted, then going into the second year, obviously they took a chance on me. So it's pretty cool to be with the team that took a chance on me. I'm looking forward to continuing this career here in St. Louis. Obviously, not often a player gets the opportunity to do that.
"The biggest thing ... was to stay here in St. Louis. I've always enjoyed it here and that was the main focus."
Parayko scored 12 points (two goals, 10 assists) and was minus-2 in 32 regular-season games. He missed 21 games from Feb. 18-April 3 because of a back injury; he scored four points (one goal, three assists) in 16 regular-season games after returning and had one assist in four Stanley Cup Playoff games.
"It's doing really good, it's getting healed now," he said of his injury. "It was nice to have a little time off, a little bit of treatment for it and everything. Back, ready to run. It's exciting. I'm looking forward to getting this year going.
Obviously last year was a little different for me personally. ... because I've never been through that in a season where [I was] away from the team and stuff with injuries. I've been fortunate that way, so I'm just happy [I'm] back and ready to go, back to normal and looking forward to just having more healthy seasons."
Selected by St. Louis in the third round (No. 86) of the 2012 NHL Draft, Parayko has scored 171 points (41 goals, 130 assists) and is plus-54 in 418 regular-season NHL games. He has scored 27 points (eight goals, 19 assists) and is plus-4 in 70 playoff games.
NHL.com staff writer Tracey Myers contributed to this report