The Saints full-back has emerged as one of the Premier League’s top performers this season with a series of impressive displays for the South Coast club.
His fine performances have alerted a number of the division’s big sides, with the likes of Manchester United and Tottenham having been linked with the 18-year-old.
However Chelsea are ready to beat their rivals to his signature with a swap deal.
The Blues are eager to tempt Southampton into selling their teenage star by offering a ready-made replacement in the shape of Bertrand, plus a significant cash payment.
Despite claims from the club that Shaw is not for sale, such a deal could be tempting, with the Chelsea defender having been dubbed the ‘new Ashley Cole’ in the past.
Chelsea are thought to be keen to hold off of making the offer until the summer, during which time Cole may leave the club.
Bertrand is also wanted by Liverpool, but a switch to` Southampton may grant him a greater opportunity of regular first-team action.