There is no direct relationship between asava and kamma beeja.
Asava are more closely related to one’s gati.
Kammma beeja are more specific. Of course they arise depending on one’s gati (or asava).
One attains Nibbana by removing asava (asavakkhaya). One’s gati are also removed at the same time. One’s kamma beeja may still be there, but they cannot bring vipaka.