The Rangers have inquired about St. Louis at times over the past two, possibly three, seasons, but have been declined.
Whether St. Louis still wants to be traded, after first requested a move roughly a month ago, remains to be seen. In the meantime, Yzerman is trying to upgrade his roster leading up to the playoffs.
With Steven Stamkos nearing a return to the lineup, the Bolts are hoping to finish the regular-season strong.
Yzerman is believed to be in the market for a mobile defenseman and a second or third line winger.
The Lightning has reportedly shown interest in New York Islanders blueliner Andrew MacDonald, Florida Panthers defenseman Tom Gilbert, Edmonton Oilers right wing Ales Hemsky and Calgary Flames right wing Lee Stempniak.