Alexander-Arnold's contract with the Reds expires at the end of the season.
However, the right-back is now free to sign a pre-contract agreement with a foreign club and Madrid appear to be at the front of the queue to snap up the England international.
Such is Los Blancos' interest in Alexander-Arnold, they made a cheeky approach to sign the defender this month as incumbent Madrid right-back Dani Carvajal remains sidelined with a torn ACL.
talkSPORT understands the Reds swiftly rejected Madrid's bid and made it clear they have no interest in losing Alexander-Arnold mid-season.
Despite their bid being turned down, Madrid will no doubt ramp up their pursuit of Alexander-Arnold as January rumbles on.
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With the winter window now open, Ancelotti was asked about the club's transfer plans.
In return, the Italian offered a rather cryptic response.
"We will see," Ancelotti said.
He added: "Talking about this in this context is more complicated, we'll see. We have a lot of games in January and we're focused on this.
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"It's not easy for me to talk about the market now.
"I don't want to talk about it because I don't think it's the right time to talk about it here.
"We'll see what happens, but I'm delighted with the squad we have."
Alexander-Arnold is one of three stars the Reds risk losing for free at the end of the season, with Mohamed Salah and Virgil van Dijk also entering the final six months of their deals.
Losing boyhood fan and academy product Alexander-Arnold would be a major blow for the Reds, especially midway through what has proven to be a dream season under Arne Slot.
Slot had a major job on his hands by taking over at Anfield from the enigmatic Jurgen Klopp.
But the Dutchman has transformed Liverpool into a free-scoring machine as they sit six points clear at the top of the Premier League at the halfway mark.
The Reds are also the only team to have maintained a perfect record after six games in the Champions League and have conceded just one goal.
Slot may not have to wait long to land his first trophy either given Liverpool are three games away from winning the Carabao Cup.
Liverpool take on Tottenham in the two-legged semi-finals, with the north London side hosting the first leg on January 5.
The Reds are no stranger to the Carabao Cup final having made it to that stage in two of the last three seasons.