The 19-year-old Welshman has made 13 appearances for Liverpool this season in all competitions and is rated as a big talent at Anfield.
But he is still not a regular at Anfield and there are suggestions that several clubs could look to snare him away in the summer.
Southampton want to sign a full-back at the end of the season and it has been claimed that the Saints are interested in Williams.
The south coast club are considering making a move for the teenage full-back during the summer transfer window.
His ability to play both as a right-back and a left-back is a big draw for Southampton who want to strengthen that area of their squad.
The Saints are planning to do a deal similar to that which saw Kyle Walker-Peters move from Tottenham to St. Mary’s on an initial loan deal and was later signed on a permanent move.
But it remains to be seen whether Liverpool are interested in letting one of their top young players leave.
Southampton failed with an attempt to sign Brandon Williams from Manchester United in January as well.