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We've taken a look at five of the most appealing ones, with a ranking for how good they would be for Liverpool.
Number five: Martim Fernandes (FC Porto)
With a $65 million (£50 million) release clause, the 19-year-old wonderkid is a regular in the Porto senior team.
Number four: Tino Livramento (Newcastle)
Newcastle United full-back Tino Livramento is one of the best young full-backs in the Premier League.
Signing one of them might not be anywhere near as costly as prizing Alexander Isak away from St James' Park, but it wouldn't be much simpler of a deal to do.
Number three: Pedro Porro (Tottenham)
The numbers suggest that the Spurs full-back would be a good stylistically similar successor for Alexander-Arnold.
And that is before even considering the fact that Liverpool would have to negotiate with Daniel Levy.
Number two: Jeremie Frimpong (Bayer Leverkusen)
The leading contender from outside the club for the role, Liverpool.com reported last week that the Dutchman was an option under consideration should Alexander-Arnold move on.
Bradley isn't as good as Alexander-Arnold but he has plenty of potential still to be exploited
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