The 22-year-old has been a key target for the club over the past few months.
Hartman even attended a game recently, but may now have to wait for his dream move.
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Per 1908.nl, Hartman has undergone surgery for a knee issue and is hoping to recover in the coming months.
Chelsea will prefer to wait and see how the Feyenoord star recovers before pursuing him in the future.
He is expected to be out of action until the start of 2025 at the very least, according to the report.