The 27-year-old is a first-team regular on the South Coast, starting each of his side's four Premier League matches so far this campaign under Russell Martin.
Despite his best efforts, Walker-Peters was been unable to help Southampton to their maiden top-flight points, meaning that they sit 19th in the league table.
Due to the summer arrival of Yukinari Sugawara from AZ Alkmaar, the Englishman has been operating on the left side of the backline during the 2024-25 term to date.
Since making the permanent switch from Tottenham Hotspur in August 2020, Walker-Peters has featured on 161 occasions for Southampton, scoring six goals.
Southampton, Walker-Peters talks break down?
According to transfer specialist Fabrizio Romano, Southampton have been dealt a major blow in their pursuit of keeping Walker-Peters on the South Coast.
The report states that discussions between the Saints and the 27-year-old over a contract extension at the club have recently broken down.
It is understood that Martin's side had offered to extend Walker-Peter's terms back in August, although the full-back did not favour the agreement.
It is claimed that a deal for the two-time international to remain at St Mary's past the end of the 2024-25 campaign is "far away" at this stage.
Walker-Peter's current contract at Southampton expires in the summer, meaning that he will be able to depart on a free transfer at the conclusion of the term.
Who are Walker-Peters's potential suitors?
With plenty of Premier League experience and a pair of England caps to his name, Walker-Peters could be an attractive option to a host of established top-flight clubs.
The full-back was recently been linked with a move back to former club Tottenham, who are in the market to increase squad depth in defensive areas.
However, with Destiny Udogie and Pedro Porro impressing in the Premier League so far, it is unclear whether Walker-Peters would receive enough game time for his liking in North London.