The Rangers have had an interest in Nash since the middle of this past season, and tried acquiring him before the Feb. 27 trade deadline.
Blue Jackets GM Scott Howson has been fielding calls for weeks, as trade talks for Nash started to pick up steam around the Stanley Cup Final.
Aaron Portzline of the Columbus Dispatch reported this morning that trade talks for Nash have heated up across the board.
The San Jose Sharks, Toronto Maple Leafs and Philadelphia Flyers are also among the teams seriously interested in Nash.