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The 39-year-old had been the favorite for a number of weeks, although Liverpool looks set to go in a different direction.
The Reds have been on the lookout for a new manager since Jürgen Klopp signalled his departure earlier this year.
Amorim emerged as a strong contender, but Liverpool now looks set to appoint Arne Slot, with a deal expected to be finalized with Feyenoord soon.
Sky Sports' Melissa Reddy highlighted the main issues with Amorim's candidacy.
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She explained: "He had ticked quite a few of the criteria to get onto the shortlist, but the big sticking point was that his playing philosophy was so different.
Remember, Liverpool play the same way through all the age groups up, so you don't want to disrupt that."
Although Amorim is out of the running, Klopp has given his nod to Slot.
It's not up to me to judge these things but it all sounds really good to me."
Liverpool.com says: Given Amorim's style was apparently a sticking point for Liverpool, you have to wonder what it would have meant if Alonso had still been in the running.
Both managers play three at the back — would that have also seen the former midfielder ruled out?
In any case, Liverpool and Michael Edwards have clearly done their homework.