Kovalchuk, who played the past five seasons in the Kontinental Hockey League, reportedly cannot sign with an NHL team until July 1 but can agree to a contract before then.
"There's nothing planned yet on a visit," Armstrong said, "but we certainly talked to his agent asking him to explore our situation and see if there's interest."
The Blues were 44-32-6 this season, one point behind the Colorado Avalanche for the second wild card into the Stanley Cup Playoffs from the Western Conference. It was the first time St. Louis failed to qualify for the playoffs since 2011.
The Boston Bruins also plan to speak with Kovalchuk's agents, general manager Don Sweeney said Wednesday.
Kovalchuk reportedly has met with the Los Angeles Kings and the San Jose Sharks. The Los Angeles Times reported he met with Kings president Luc Robitaille and general manager Rob Blake last Friday, and TSN said he met with the Sharks on Monday.
Kovalchuk hasn't played in the NHL since the 2012-13 season, when he had 31 points (11 goals, 20 assists) in 37 games for the New Jersey Devils. Playing for St. Petersburg SKA, Kovalchuk led the KHL in scoring this season with 63 points (31 goals, 32 assists) in 53 games. He has 285 points (120 goals, 165 assists) in 262 games during the past five seasons in the KHL.
Kovalchuk has 816 points (417 goals, 399 assists) in 816 NHL games over 11 seasons with the Atlanta Thrashers and Devils. He scored at least 40 goals in six straight seasons from 2003-04 to 2009-10, including an NHL career high 52 twice for the Thrashers, in 2005-06 and 2007-08.