The 18-year-old has been, arguably, the most impressive young player in the Premier League this season, and is now considered to be one of the high-flying Saints’ key men despite his youthful age.
His performances have attracted much interest from some of the division’s top sides, with Manchester United having been credited with a serious interest on several occasions.
But it could be Chelsea who make the first move, with Jose Mourinho becoming increasingly concerned by current first-choice left-back Ashley Cole’s form and fitness.
‘The Special One’ has been fielding Cesar Azpilicueta – a right-sided defender – in the position of late, and is believed to be on the lookout for a long-term option for the role.
The teenager is thought to be their top target, with the London club confident that a £20m offer for a relatively unproven talent could be too good for Southampton to pass on.
To further sweeten the deal Ryan Bertrand could be offer in exchange, although the left-back is also wanted by Liverpool and Everton.
Cole is expected to be given a one-year contract extension, which could be used as a way of bedding Luke Shaw into life at the club gradually.