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But Alonso and Amorim are two of the more intriguing options who are gathering pace.
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If Liverpool settle on either Alonso or Amorim, the club would have to pay a hefty fee to meet their release clauses.
The current world record fee to take a manager from one club to another belongs to Nagelsmann, who moved from RB Leipzig to Bayern Munich for $28m (£22m/€25m) back in 2021.
Liverpool faces paying close to that amount if it wants either Amorim or Alonso to succeed Klopp.
Xabi Alonso
Xabi Alonso is hot property as a result of his success as Bayern Leverkusen manager.
The midfielder joined the club for $13.6m (£10.7m/€12.5m) not adjusted to inflation when Liverpool signed him from Real Sociedad back in 2004.
Rúben Amorim
Rúben Amorim has carved out a reputation as one of the hottest properties in management at Sporting CP, but his contractual situation in Lisbon appears far more complex than Alonso’s.
Back in 2022, he was linked with Premier League club Aston Villa after it fired Liverpool legend Steven Gerrard.
Ruben Amorim has carved out a reputation as a highly-rated young manager at Sporting CP.
When considering how much is spent on transfer fees for players, the figures being talked about for Alonso or Amorim are a drop in the ocean for a club like Liverpool