Dest has been on-loan this season with PSV Eindhoven, where he hopes to sign permanently.
He confirmed: "Unfortunately I tore my anterior cruciate ligament and will soon have surgery.
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"I am going to do my best to get back to my level as soon as possible. It will be a very hard period for me, but I know it will only make me stronger.
"I will return to make you proud."
PSV can sign Dest permanently for 10m.