The England international is one of three Liverpool stars out of contract at the end of the season, along with Virgil van Dijk and Mohamed Salah.
Real Madrid have emerged as the frontrunners to sign Alexander-Arnold if he fails to agree a new contract with the Premier League leaders.
Los Blancos are keen to strengthen the right side of defence, especially as they have seen their squad depth tested by Dani Carvajal's long-term knee injury.
Real Madrid register Alexander-Arnold interest
According to talkSPORT, have made contact with Liverpool to inform them of their desire to sign Alexander-Arnold next summer.
There is no requirement for Real Madrid to formally register their interest, but they want to be respectful to the Merseyside club.
As it stands, the Liverpool right-back will be able to sign a pre-contract agreement with an overseas club in January.
There is a suggestion that Real Madrid are hopeful that Jude Bellingham's friendship with Alexander-Arnold can help them secure the right-back's signature.
However, Liverpool have not given up hope of agreeing a new contract to retain the services of their academy product.
Can Liverpool afford to lose Alexander-Arnold?
Liverpool may still be keen to keep Alexander-Arnold, but they have failed with their previous attempts to agree a new deal with the defender.
If they fail to make progress in negotiations, Liverpool may have to start contemplating the prospect that Alexander-Arnold could leave the club on a free transfer next summer.
From a financial view, the Reds would be disappointed to see Alexander-Arnold walk away for nothing, but his departure may not be devastating from a sporting perspective.
The 26-year-old is undoubtedly a top-quality full-back, but his teammate, Conor Bradley has demonstrated that he is ready to become Liverpool's first-choice right-back.
The Northern Ireland international showcased his quality in Wednesday's Champions League win over Real Madrid, producing a stellar performance to thwart Kylian Mbappe and co.
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