As a result, the Rangers will have some holes to fill in their lineup.
According to the New York Post, the Rangers are interested in free agent defenseman Mark Fayne.
Fayne, 27, will hit the open market in just over 12 hours and has attracted the interest of several teams, including the Rangers and Edmonton Oilers.
The Post also suggests the Rangers could do after Ryan Carter to replace Boyle.
Rangers GM Glen Sather is believed to have kicked the tires on free agent center Paul Stastny, who will field formal offers once the free agent doors swing open at noon ET on Tuesday.