Mills progressed through the Rams' academy and has made two first-team appearances for the Pride Park outfit He has had two loan spells this season, with Blue Square North side Solihull Moors and Burton's League Two rivals Macclesfield.
The 19-year-old played and scored as a trialist for Albion in a 2-1 reserve-team victory over Sheffield Wednesday at the Pirelli Stadium on Tuesday.
