Manchester United boss David Moyes could make a move for Chelsea left-back Ashley Cole in the summer, reports the Mirror.
Both Manchester United and Chelsea appear to be in the market for Shaw, who could cost as much as £35 million.
And if the Red Devils do miss out in the Saints youngster, the Manchester United boss will be hoping to sign Cole on a free as the Chelsea star's contract runs out at Stamford Bridge in the summer.
Cole has struggled for chances at Chelsea this season and recent reports have suggested that he won't be offered a new deal to stay at the club. This could pave the way for him to move to Manchester United in the summer.
If Cole was to join Manchester United then he would join up with his former Chelsea teammate Juan Mata at the Theatre of Dreams.
However it remains to be seen as to whether the Premier League champions will bring the England international to Old Trafford in the next window.