If someone has an insatiable desire for something, they want as much of it as they can possibly get. The public has an insatiable appetite for stories about the famous = voracious. always wanting more and more of something insatiable appetite/desire/demand etc (for sth) (insatiabilis, from satiare )
impossible to satiate or satisfy; "an insatiable appetite"; "an insatiable hunger for knowledge"
Not satiable; incapable of being satisfied or appeased; very greedy; as, an insatiable appetite, thirst, or desire