The 22-year-old is valued at £12million by Tottenham, who are pushing for a permanent deal over a loan.
Kyle Walker-Peters has attracted several clubs after making just five Spurs outings this season
Southampton manager Ralph Hasenhuttl is leading the way to sign the out-of-favour defender
Saints coach Ralph Hasenhuttl wants two new full-backs and hopes a deal can be reached this week.
Southampton are also understood to have asked about Nottingham Forest’s £18million-rated Matty Cash.
Palace have asked about Walker-Peters but are considering highly-rated Nathan Ferguson at West Brom as an alternative.
Ferguson has been linked with a host of clubs in the Premier League and Europe during a promising first senior season with the Championship pacesetters.
Forest full-back Matty Cash is also interesting Southampton and holds an asking price of £18m
West Brom prodigy Nathan Ferguson could appeal to Palace as an alternative to Walker-Peters