Marc Stein of the New York Times reported the Kings would also receive draft compensation.
ESPN's Brian Windhorst said on The Jump that the Cavs are "at the one-yard line" to dealing for Hill, via Ali Thanawalla of NBC Sports Bay Area.
Problems continue to mount in Cleveland this season. The three-time defending Eastern Conference champions have gone 3-9 in their last 12 games and rank 28th in defensive efficiency, per Basketball-Reference.com.
Frustration appeared to boil over Monday when Wojnarowski reported the Cavaliers held a team meeting prior to practice that included several players challenging Kevin Love's illness that caused him to leave Saturday's game against the Oklahoma City Thunder early.
Neil Greenberg of the Washington Post noted Hill ranks in the top 13 percent of NBA defenders with 0.68 points per possession against the pick and roll, but his 0.87 points per possession as the closest defender is worse than Isaiah Thomas (0.70).
Shumpert has been out since November after having arthroscopic knee surgery. Frye is averaging a career-low 4.1 points per game, though he's shooting a career-best 50.4 percent from the field.