He is in the final season of a four-year, $13.45 million contract and would have been an unrestricted free agent this summer.
Steen leads the Blues in goals (22) and points (36) this season. He is tied with Corey Perry of the Anaheim Ducks for second among all NHL players with 22 goals, trailing the Washington Capitals' Alex Ovechkin, who has 28.
The 22 goals are two fewer than Steen's career high for a season, set in 2009-10 with the Blues.
Steen was acquired in a trade with the Toronto Maple Leafs on Nov. 24, 2008. In 570 regular-season games for the Maple Leafs and Blues, he has 145 goals and 339 points. Steen has four goals and seven points in 19 Stanley Cup Playoff games.