The Royals will get left-handed reliever Josh Taylor in exchanged for Mondesi and a player to be named later, sources told ESPN.
Mondesi, 27, has played in only 50 games over the past two seasons because of injuries.
He was limited to 15 games during the 2022 season after suffering a torn anterior cruciate ligament in his left knee on an attempted pickoff play in April. He played in only 35 games in 2021 because of left hamstring and left oblique injuries.
Mondesi was batting .140 (7-for-50) with five stolen bases in five attempts when his 2022 season abruptly ended. In seven MLB seasons, he has a .244 batting average with 38 home runs, 157 RBIs and 133 stolen bases.
Taylor missed the 2022 season because of back issues. In three MLB seasons, he has a 3.9 ERA with 129 strikeouts and 44 walks in 102⅓ innings.