The 27-year-old was one of the club's star performers during their most recent Premier League campaign of 2022-23, when the Saints' decade-long spell in the top flight ended with relegation.
Walker-Peters decided to stay put on the South Coast in the second tier, helping Southampton to turn around their fortunes under the fresh leadership of Russell Martin.
The full-back started 43 matches in the Championship for the Saints last term, with Martin's troops earning an immediate return to the Premier League via the playoffs.
Since making the permanent switch from boyhood club Tottenham Hotspur to St Mary's Stadium in August 2020, Walker-Peters has made 161 competitive appearances for Southampton, scoring on six occasions.
Southampton struggling to convince Walker-Peters to stay?
According to Football Insider, Southampton could be set to lose one of their key first-team players during the summer transfer window of 2025.
The report claims that the Saints face an uphill battle as they attempt to retain the highly-valuable services of Walker-Peters past the conclusion of the season.
With the 27-year-old in the final 12 months of his contract, the defender is able to join a new employer on a free transfer at the end of the current campaign.
It is understood that Southampton and Walker-Peters have entered talks over a new deal for the player on the South Coast, although movement towards an agreement is slow.
The Saints are supposedly unlikely to convince the full-back to stay at the club, meaning that his association with the top-flight strugglers is set to end in the summer.
Southampton's start and Walker-Peters's new role
Martin's troops have struggled massively since returning to the top table of English football, losing each of their first four matches in the division.
The latest of those defeats arrived at St Mary's against Manchester United on Saturday, when goals from Matthijs de Ligt, Marcus Rashford and Alejandro Garnacho sealed maximum points for the Red Devils.
Despite traditionally being used as a right-back, Walker-Peters has showcased his versatility at the beginning of the 2024-25 term, operating on the left side of Southampton's defence.
Such an alteration for the former Spurs man has allowed summer arrival Yukinari Sugawara to slot into the defence on the right, with the Japan international netting his side's only goal so far in the 3-1 defeat at Brentford prior to the international break.