The 50-year-old is rumoured to be a candidate for Arne Slot's backroom team at the Premier League champions, following John Heitinga's departure to Ajax.
Van Bronckhorst, who has been working in the media since leaving Besiktas last November, would join fellow Dutchman Slot at Liverpool.
However, former Dutch footballer Hans Kraay Jr believes this move would signal the end of van Bronckhorst's career as a manager.
In his column for Voetbal International, Mr Kraay wrote: "At Feyenoord, apart from his first period, when he needed Dick Advocaat to keep himself in the saddle, he revealed that he quite enjoyed being a head coach.
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"In any case, if you are at a club that often wins, it is a much more enjoyable job than being a coach at RKC or Almere.
"But in Feyenoord's championship year, with all the stress that comes with being a coach, he was quite relaxed, open and jovial towards us.
"The championship helped a lot, of course.
"After that, van Bronckhorst spread his wings and left for Rangers.
"After a good start, it became quite stressful there.
"I think this assistantship to Arne Slot means the end of his career as head coach, and also of the life in which you spend 168 hours a week on football."