The Melwood academy product is in the final year of his Reds contract, with a potential summer transfer looming on the horizon.
Alexander-Arnold, now 26, has been heavily linked with a move to Real Madrid, where his England teammate and close friend Jude Bellingham plays.
Los Blancos are looking for a new right-back with first choice Dani Caravajal currently out injured with an Anterior Cruciate Ligament rupture.
But while Alexander-Arnold's contract runs down and question marks remain over his future, he has insisted fans will not be finding out any details of any talks anytime soon.
Nevertheless, hearing the hometown boy even mention talk of a possible extension will give supporters hope the Scouse star could stay.
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Speaking to Sky Sports in a sit down interview, he said: "I have been at the club 20 years now and I have signed four or five contract extensions… and none of those have been played out in public.
"This one won't be either."
Despite his future being currently unknown, the England international acknowledged he has been enjoying playing under new boss Arne Slot since he took Jurgen Klopp's place in the Liverpool dugout.
The defender said: "I could tell from the first time I met him that I was going to enjoy playing under him and being a part of this.
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"I'm feeling like I'm going to get better and improve.
"I could tell he was football obsessed and the level of detail was incredible."
Slot has led Liverpool to the top of the Premier League and the new-look Champions League table in his first season in charge.
He had a huge boots to fill after he replaced Klopp, who stepped down as Reds boss after eight years at the end of the last campaign.
Alexander-Arnold has played 18 games this season, grabbing four assists in all competitions in that time.
He suffered a hamstring injury in November but has since recovered, proving himself as a key member of the Liverpool first-team, as well as his leadership role as the club's vice-captain.
Two other of Slot's stars, Mohamed Salah and Virgil van Dijk, are also out of contract at the end of the season, with their futures also unclear.
All three players won the Champions League under Klopp in 2019, as well as the Premier League in 2020.
Liverpool face Fulham at home on Saturday afternoon as they look to extend their lead at the top of the league after their Merseyside derby against Everton was postponed last week.