With his contract expiring at the end of the season, Achterberg is ready for a new challenge.
He has spent the past 15 years with Liverpool, working under several coaches.
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Jack Robinson, Achterberg's understudy, may well remain or could even take his spot.
Manager Jurgen Klopp and assistant managers Pep Lijnders and Peter Krawietz are also departing.
Liverpool's CEO of football Michael Edwards will be tasked with finding replacements.