The Blues are pressing the accelerator in the transfer market as Thomas Tuchel looks to rebuild his defensive options following a series of departures from Stamford Bridge.
They are expected to complete the signing of Marc Cucurella from Brighton, but thoughts are already turning towards further recruits to follow the Spaniard.
Inter’s Denzel Dumfries is of interest to Chelsea and at the top of their list, while Southampton’s Walker-Peters is a name which has been discussed internally at the club.
Walker-Peters would arrive at Chelsea with the added benefit of being Premier League proven.
However, Southampton are unlikely to want to let the defender go and Chelsea may have to work hard to make a deal for him happen.
The 25-year-old made 32 appearances in the Premier League for Southampton over the course of last season, with Saints boss Ralph Hasenhuttl a big fan of what he brings to the team.
Southampton have Walker-Peters locked down on a contract which still has another three years left to run.