Walker-Peters has struggled for game time so far this season, making just three Premier League appearances.
According to The Sun, the 22-year-old will will join the Saints on loan until the end of the season, with Ralph Hasenhuttl keen on reinforcements in the full-back areas.
Crystal Palace were also said to be interested, but seem to have lost out to the South coast club.
The England youth international can play at both right-back and left-back, but will hope to play in his preferred position on the right due to the injury suffered by Cedric Soares. body check tags ::