Witham turned out for Albion's reserve-team on Tuesday afternoon in their final fixture of the season at the Pirelli Stadium against Port Vale.
The midfielder played the full 90 minutes alongside Seanan Clucas in a 3-0 win for Burton.
Witham has progressed through Derby's academy system to play reserve-team football for the Rams this season.
Albion caretaker manager Gary Rowett said: "Alex is a young midfield player with something to offer and he is certainly worth a look."
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