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The 26-year-old right-back, who has been with the Reds since the 2017-18 season announced on Monday that he will exit Anfield, with the transfer to Madrid to be finalized on July 1.
With his contract expiring this summer, Alexander-Arnold has been free to negotiate with clubs outside the UK since January.
Despite an approach from Real in January, Liverpool had remained silent on the matter.
Many Liverpool fans seem to echo Arne Slot's sentiments who agreed with Alexander-Arnold's assessment, remarking: "I think it's going to be a bright future for him because he's a very good player and very good players [are] what we need here at Liverpool.
He's done - last season especially - really well when he had to replace Trent, and now Trent has played a lot.
"But he is a very good player and although he has big competition from Trent, normally very good players find their way into the team.
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"All of a sudden you're [getting told] "alright, this is your position", that's when you start going "hey, I could play 40 games a season..."
Keane the asked Jamie Carragher if he would 'trust' Bradley as Liverpool's main right back, with the Anfield icon responding: "I think he has done well enough so far that Liverpool doesn't need to get someone in for $50-$60M, and instead get someone for $20M