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Wirtz spent the summer on holiday with another new signing from Leverkusen, Jeremie Frimpong, who joined for £29.5m.
Elsewhere, Liverpool completed the £40m signing of Milos Kerkez from Bournemouth.
The left-back was signed after goalkeeper Armin Pecsi joined from Puskas Akademia for £1.5m.
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And Liverpool continue to be linked with further additions amid reports that they are looking to bolster their defence and attack.
Crystal Palace centre-back Marc Guehi has been linked for some time with the Eagles reportedly wanting at least £40m for him.
The Reds face Palace in the Community Shield on August 10 at Wembley Stadium.
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Meanwhile, Real Madrid star Rodrygo has been linked with Liverpool and Arsenal this summer.
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