Like Mohamed Salah and Virgil van Dijk, Alexander-Arnold has entered the final 12 months of his Liverpool contract.
As it stands, the England international would be allowed to discuss a pre-contract agreement with foreign clubs from January 2025.
The defender's contract situation has led to links with reigning European champions Real Madrid, who could offer Alexander-Arnold the opportunity to play alongside his England teammate and friend Jude Bellingham.
Los Blancos seemingly view Alexander-Arnold as someone who could be a long-term successor to Euro 2024 winner Dani Carvajal.
Slot addresses Alexander-Arnold future
With Real Madrid waiting to pounce, Liverpool are allegedly prepared to offer Alexander-Arnold a bumper contract to extend his stay with the Merseyside club.
Ahead of Liverpool's pre-season friendly against Real Betis, Slot was asked whether he was confident about the club's chances of tying Alexander-Arnold down to a new deal.
Slot told reporters: "My answer will probably be a bit boring, I think it is the same answer you have heard in the last five six, seven years. That contract situation is not discussed at this place, but just keep trying I would say!"
The Reds will kick off their pre-season tour of the USA in Saturday's meeting with La Liga side Real Betis in Pittsburg.
However, Alexander-Arnold will not be involved in the friendly because he is one of several star names who are enjoying some time off following a busy summer of international football.
Slot will be desperate to keep Alexander-Arnold
While he was reluctant to comment on any contract talks, Slot will undoubtedly be keen to retain the services of one of the Premier League's best full-backs.
The Dutchman will know the importance of Liverpool keeping the experience and quality of key players like Alexander-Arnold if he is to reproduce the heights of the Jurgen Klopp era.
The 25-year-old has made 310 competitive appearances for his boyhood club, scoring 19 goals and providing 81 assists.
The defender has helped Liverpool win the Premier League, FA Cup, Champions League, FIFA Club World Cup, UEFA Supercup and two EFL Cups.