Williams has been at Liverpool since 2009 when he joined the club's Under-9 side and graduated from the academy when he made his first-team debut 10 years later.
However, the Daily Mail reports that the Welsh international has a desire to play regular first-team football and is prepared to exit Anfield in search of this.
The future of the full-back is likely to be resolved following Wales' Euro 2020 campaign, which was extended by a week as Rob Page's side qualified for the last 16 with the help of Williams, who made his first start in the tournament against Italy on Sunday.
Since making his Liverpool debut in 2019, Williams has gone on to make 25 appearances for the Reds. body check tags ::