The 25-year-old player is currently in the last year of his contract at Anfield. If he doesn't sign a new deal before January, he will be free to discuss terms with clubs from abroad for a potential free transfer in the summer.
Real Madrid have been heavily linked with a move for Alexander-Arnold, with key figures at the Bernabeu believed to be monitoring the situation.
Liverpool learn key Trent Alexander-Arnold demands
Alexander-Arnold - who FourFourTwo have ranked as the very best right-back in the world right now - has been at Liverpool since he was six years old, breaking into the first team in 2016 and has subsequently played more than 300 games for his boyhood club.
A free transfer exit next summer would, therefore, be a wrench for both club and player, but Alexander-Arnold has reportedly told the Reds what they must do in order to keep him at the club.
According to Football Insider, the defender has told Liverpool that he will need assurances that they are able to both match his trophy ambitions and to also keep strengthening the side in the transfer market if he is to stay.
This echoes the player’s quotes from earlier this month when he was directly asked about his future.
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“The most important thing is always trophies. I want to win trophies,” he said. “We were close to the title last season and we got a cup. The (quadruple) was on for a while I suppose.
“This season we are looking really good, it is still early days, but we need a lot of consistency. It will be difficult but we are looking to win as many trophies as we can.”
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In FourFourTwo’s opinion, a player of Alexander-Arnold’s quality and drive is right to have such lofty ambitions and it is up to Liverpool to meet them, otherwise they risk losing a player valued at €70million by Transfermarkt for nothing next summer.
The Reds will know that Real Madrid are waiting in the wings, having just won the Champions League and signed Kylian Mbappe to prove that trophies and transfers are all par for the course at the Bernabeu.