The 26-year-old is believed to be Los Blancos' top target to replace the long-serving Dani Carvajal, who is expected to miss the rest of the season due to a severe knee injury.
Reports on Friday claimed that Liverpool were 'resigned' to the fact that Alexander-Arnold would not be renewing his Anfield contract, which is due to run out at the end of the season.
Should the two parties not come to an agreement over an extension before New Year's Day, Alexander-Arnold could open pre-contract talks with foreign clubs in January, which may be Liverpool's last chance to garner a fee for their youth product before a possible free transfer next summer.
However, speaking to the media before his side's La Liga clash with Celta Vigo on Sunday, Ancelotti insisted that he had full faith in Lucas Vazquez and Eder Militao to fill the Carvajal void for the remainder of the season, and he does not anticipate any January arrivals.
Ancelotti plays down talk of January Alexander-Arnold move
"We have Lucas Vazquez, we trust him. Then there's Eder Militao. I see him well as a right back, yes," the Evening Standard quotes Ancelotti as saying.
"I have not asked for new signings in January as last year we managed the situation well. Signing a player who will be good for Real Madrid is not easy. At the moment we are not thinking about it."
Alexander-Arnold broke his silence regarding his contract situation earlier this month but was non-committal to either Liverpool or Real, affirming that he wanted to play for a team that could match his silverware ambitions.
The right-back also refused to commit himself to any club beyond the summer of 2025, simply stating that he was preparing to represent Liverpool for the remainder of the season before making a decision on his future.
Reds boss Arne Slot has been pressed for an update on Alexander-Arnold's situation most weeks, but he only offered a curt reply when asked on Friday, saying: "No. I can't tell you anything about that."
What about Virgil van Dijk and Mohamed Salah?
Alexander-Arnold's uncertain situation is not the only unwelcome distraction for Liverpool boss Slot, as it is well-documented that Virgil van Dijk and Mohamed Salah are out of contract next year too.
It has been a little over six weeks since Salah made his bombshell admission that he was prepared for this season to be his "last" at Liverpool, but he is said to be keen to stay on for a little while longer, despite interest from the financial powerhouses of Saudi Arabia.
There has been little in the way of firm updates regarding Salah's contract situation, though, and the same goes for 33-year-old captain Van Dijk, who is relaxed over his future at Anfield.
However, Liverpool are said to have earmarked a young La Liga defender as a potential replacement for Van Dijk, who was released early from Netherlands duty ahead of Sunday's blockbuster Premier League clash with Chelsea.