The defender has impressed throughout the season, having featured in 29 Eredivisie games for the newly promoted team, who are challenging for a Europa League playoff spot in the final two weeks of the campaign.
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However, Ernest Faber's men suffered a blow as Kane went down in the late stages of Wednesday's 2-0 defeat to PEC Zwolle and was stretchered off the pitch.
An MRI scan the following day revealed that the 22-year-old has a tear on his anterior cruciate ligament. The defender will be out of action for the remainder of the season and returned to London on Friday.
Kane has been part of Chelsea's setup for 15 years and had loan spells at Preston, Blackburn Rovers, Bristol City and Nottingham Forest before his temporary move to Netherlands.