The 16-year-old rejected a scholarship offer at Anfield after his schoolboy registration expired last month, opting instead for a switch to north London that saw off interest from Manchester United, Chelsea, Bayern Munich and Borussia Dortmund, according to the Daily Mail.
Because Joseph moved before signing a professional contract, Liverpool are owed a development fee rather than a conventional transfer sum. With the two clubs unable to agree that figure, the case will be settled by the Professional Football Compensation Committee, which will weigh several factors in reaching its decision: the player's age and playing record, his length of time at Liverpool, the status of both clubs, and the terms each side offered him.
It is the second such dispute to make headlines this year. In February, Liverpool were ordered to pay Chelsea £2.8m in compensation after signing winger Rio Ngumoha, who left Chelsea's academy in September 2024 in search of a faster route to the first team.
Ngumoha has since made 30 appearances for Liverpool, scoring twice, having turned down contract offers from Chelsea to make the switch.
An England youth international, Joseph has scored eight goals in nine appearances for the Under-16s and made his Under-18s bow for Liverpool last season. His arrival continues a busy summer of academy recruitment for Arsenal, who have already added Tottenham defender Elijah Upson and Crystal Palace forward Mylo Bernard after the latter's schoolboy deal expired, while also working on a deal for Cardiff City's Axel Donczew, who became his club's youngest-ever first-team player at 15 years and 234 days old when he made his debut in October.
The recruitment drive follows a mixed summer for Arsenal's own academy, having lost midfielder Mishel Nduka to Manchester City after he opted against staying to continue his development in north London.
Even so, the club can point to a fast pathway into Mikel Arteta's first team: teenagers Max Dowman and Marli Salmon both received significant senior exposure during pre-season, evidence Arsenal will hope encourages Joseph and their other young recruits to follow suit.