Kuemper, with a $5.25 million annual salary until 2026-2027, completes the goaltending team alongside David Rittich.
Marner, 27, earns $10.9 million annually and is under contract until the end of the next season but has a no-movement clause.
The Maple Leafs could offer him a contract extension, but if they don't, the Kings might attempt to acquire him to strengthen their lineup.