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One of those being linked may already have the door open to a move.
Here is the Liverpool.com verdict on the transfer gossip to emerge around the Reds on Tuesday, including an update on Dean Huijsen that may well interest Liverpool after Hughes' trip at the weekend.
Dean Huijsen (Bournemouth)
Dean Huijsen has a "confirmed" release clause of $63 million (£50M) in his contract at Bournemouth, according to Fabrizio Romano.
The new Liverpool home shirt for the 2024/2025 season features a chrome yellow pattern design and is a modern take on the legendary '84 home shirt - a season which saw the Reds become European Champions for the fourth time in Rome and the first English Club to win a treble of major honours.
Liverpool.com says: Huijsen is absolutely a player Liverpool should be watching right now
In fact, the Reds perhaps should have taken a gamble on him last summer when it was clear he was going to be leaving Juventus.
Since he's joined Bournemouth, he hasn't looked out of place in the Premier League, even at such a young age in such a high-pressure position at center-back
Whether he's ready to step into Van Dijk's shoes immediately is up for debate, but he does look an exciting prospect.
Florian Wirtz (Bayer Leverkusen)
Liverpool and two other Premier League clubs have made contact with Florian Wirtz's camp, with the Bayer Leverkusen star looking likely to be on the move in the summer, according to TBR Football.
The Reds, Arsenal and Manchester City are all said to remain in contact with the 21-year-old, who is valued at $110 million (£87M)
It's claimed Wirtz has not ruled out a move to the Premier League, although Real Madrid and Bayern Munich are pushing hard for his signature, which will make things trickier for Liverpool.
Liverpool.com says: Signing Wirtz would be a real coup for Liverpool, but you can absolutely guarantee Europe's heavyweights will be looking at him
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