Miller, 33, is in the final year of his contract and is set to become an unrestricted free agent July 1.
The Blues acquired Miller from the Buffalo Sabres on Feb. 28, along with forward Steve Ott, in exchange for goalie Jaroslav Halak, right wing Chris Stewart, prospect William Carrier, a 2015 first-round draft pick and a 2016 conditional third-round draft pick.
Speaking to the media following Sunday's elimination game to the Chicago Blackhawks, Miller suggested that he has interest in re-signing with the Blues.
"We'll have to see where we're at and see how they feel about me," Miller said, as quoted by ESPN's Craig Custance via Twitter. "I definitely like St. Louis."
Miller made $6.25 million this season and will likely sign a multi-year contract worth around that same annual figure.
It has been widely speculated that Miller may look to sign closer to his off-season home near Los Angeles.
With the Anaheim Ducks unlikely to re-sign goalie Jonas Hiller this summer, Miller may look to sign in Orange County, if the Ducks are interested.