The agreement with Kennedy, which reportedly would include an opt-out after the second year, would cost the Royals their first-round Draft pick in 2016.
Kennedy's signing comes on the heels of the Royals retaining the face of their franchise, Alex Gordon, with a four-year, $72 million deal last week. They also reportedly are in agreement on a two-year, $17.5 million pact with All-Star center fielder Lorenzo Cain that would wipe out his final two arbitration years.
The Royals have been linked to Kennedy for weeks, and his presence would bolster what is becoming a deep rotation.