The 21-year-old spent the second half of last season on loan with Championship winners Fulham, where he recorded two goals and two assists in 14 league appearances.
Following the arrival of Calvin Ramsey from Aberdeen, Williams could now be allowed to leave Liverpool this summer in search of regular first-team football.
According to Sky Sports News, via the Daily Mail, the Saints have enquired about signing Williams on a permanent deal this summer, with Liverpool valuing the full-back in the region of £20m.
Fulham, Nottingham Forest and PSV Eindhoven are also keen to sign the Wales international, who has three years remaining on his contract at Anfield.
With Valentino Livramento set to miss the rest of 2022 with an ACL injury, Southampton have identified Williams as a potential target to bolster their options at right-back.
Williams has made a total of 33 appearances for the Reds since his senior debut in 2019, including just six starts in the Premier League.