The Daily Mirror is reporting that both the Blues and Spurs are pondering summer moves for the 24-year-old defender as both London clubs look to strengthen their squads ahead of next season.
The same report, though, says that Everton have also joined the race for the signature of the Newcastle United skipper.
The defender has been in good form for Newcastle United this season and has scored three goals in 32 Premier League games for the Magpies.
He is tied to Newcastle until 2023 after signing a new six-year contract at St James’ Park back in October.
Chelsea FC are likely to be on the lookout for a number of signings this summer after a largely disappointing second season under Antonio Conte at Stamford Bridge.
The Blues have struggled to produce consistent form in the top flight this term, leaving them in fifth place heading into the final game of the campaign.
Chelsea FC will look to try and end the season with a trophy by beating Manchester United in the FA Cup final at the end of the month.
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