The German club value the player at €150m, which equates to just over £126m.
Bayern Munich and Manchester City are also trying to sign the 22-year-old, who was among one of the Bundesliga’s most impressive performers last season.
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Up until a week ago, the Premier League champions believed the player wanted to stay in Germany but they’ve since been told he favours a move to Liverpool.
Wirtz, who has spent his entire senior career at Leverkusen, scored 10 goals and registered 12 assists in 25 starts as his side finished runners-up to Bayern Munich, a year on from winning a league and cup double.
The British record transfer fee currently stands at £107m, paid by Chelsea to Benfica for Enzo Fernandez in 2023.
Follow the transfer window on Sky Sports
The first of two summer transfer windows is upon us – and there is no better place than Sky Sports to get all the latest transfer news and rumours.
Use the Sky Sports app and website for all your updates in our dedicated Transfer Centre and Premier League club blogs, plus live Q&As with our reporters throughout the summer.
The Transfer Show returns to Sky Sports News from Sunday June 1 for the start of the pre-Club World Cup window and will then be on every weeknight at 5pm and 7pm until the deadline on Tuesday June 10.
The summer transfer window will open again on Monday June 16 until Monday September 1 – with the deadline brought forward to 7pm this year
