ESPN first reported the negotiations.
Rose, 28, is a point guard and three-time All-Star who won the MVP with the Bulls in the 2010-11 season. He averaged 18 points and 4.4 assists in 64 games for the New York Knicks last season.
The most the Cavs can offer Rose is $2.5 million from what's remaining of the team's mid-level exception to the salary cap. Cleveland could also offer him the veteran's minimum -- which for him would be $2.1 million.
The Cavs already signed one veteran back-up point guard -- Jose Calderon -- to a league minimum deal. But sources said Calderon's best role would be as a third point guard, and there is also the chance that Rose and Kyrie Irving could start in the same backcourt.
Second-year player Kay Felder's contract is not fully guaranteed for this season. Cleveland has one available roster spot, plus two two-way contracts for G League players (or players with less than four years of NBA experience).
The Cavs of course already have a three-time MVP in LeBron James.
Rose's career has been hampered by knee injuries, which cost him all of the 2012-13 season, about half of the 2011-12 campaign and all but 10 games of the 2013-14 season.
Rose is averaging 19.5 points and 6.0 assists for his eight-year career. He played on a one-year, $21.3 million deal with the Knicks last season.
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