The Knicks have had internal discussions recently about trading for Rose, league sources tell ESPN.
The Bulls' interest in trading Rose, 27, is unknown at this point. The Knicks do not have many strong trade chips outside of Carmelo Anthony, Kristaps Porzingis and future first-round draft picks.
Both Knicks coach Jeff Hornacek and GM Steve Mills have said that the Knicks are interested in upgrading their point guard position in the offseason. The Knicks' incumbent starting point guard is Jose Calderon, while other potential point guards include second-year guard Jerian Grant and free-agent signee Tony Wroten.
Rose will be a free agent after the 2016-17 season. He averaged 16.4 points on 42.7 percent shooting and 4.7 assists in 66 games last season.
The six-year veteran has appeared in just 50 percent of the Bulls' regular-season games over the past four years because of various injuries, including two major knee surgeries.
What could Rose bring to the Knicks?
ESPN Knicks reporter Ian Begley talks about the Knicks' interest level in acquiring point guard Derrick Rose, as well as whether they have enough to entice the Bulls into a trade.