The Dutchman, 21, left Ajax a year ago to join Burnley.
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Banel has now moved to Derby on loan until the end of the season.
Rams boss John Eustace said: "He is a young, exciting player and he has a point to prove.
"He is very hungry and wants to do well. To leave a Premier League club at this stage to come to a Championship team shows his ambition to really showcase himself."
