A beverage discharge disposition comprising a discharge casing (1) configured so that can be provided in the front region of a beverage preparation machine (20), including the option of supplying milk and frothed milk, whereby said discharge casing (1) presents a milk circulation disposition (2) that is characterized in that presents a simple and compact construction adapted so that can be attached in removable manner to an attached part of said discharge casing (1) and to provide an ergonomic use of said beverage preparation machine (20). Also, a beverage preparation machine (20) presenting an optimized beverage discharge disposition according to the present invention.