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The Reds have agreed to sell Alexander-Arnold for €10million (£8.5m) to the European Super League advocates so he can be available for the controversial tournament in the United States in mid-June.
The 26-year-old was due to leave on a free transfer at the end of June.
Real will therefore take over the final month of Alexander-Arnold's Anfield contract, making the deal worth £10m in total to Liverpool for a player they were set to lose for nothing
But the Reds have been told by former England international Gabriel Agbonlahor they should have held firm and made a point by refusing to bow to Real Madrid's demands no matter what the cost.
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“Do you know what I would have done?" said Agbonlahor.
"I would have loved it - and I’m sure Liverpool fans would agree - (had they said) stuff you, you’ve gone after our player sneakily, you’ve made a deal for him to say he's going to Real Madrid, you’ve cost us £100m, he’s a £100m player at a great age, you can wait until July 1 and he’s going to miss two games of the Club World Cup, how about that?
"You think you can bully everyone, Real Madrid, biggest club in the world, but you’re not bullying Liverpool.
"Yes, £10m, great money, it can go towards transfers.
But sometimes I look at it and think wouldn’t it be nice if Liverpool said ‘nah, he’s not going to play a game for you until July 1'.
"You you think you can get anything you want, Real Madrid.
You've got (Kylian) Mbappe on a free transfer, you've got Trent on a free, and now you want him you're offering £10m for a £100m player."
Speaking to talkSPORT, the November 2007 Premier League player of the month added: “I wouldn’t have taken it.
I’d have said ‘no, you went and sneakily spoke to Trent, you went and turned his head, he’s left his boyhood club on a free transfer, now because you’ve got this tournament and you want to show him off and used to playing before the season starts’.