United paid £30m for Shaw in 2014, but the left-back's game time has been limited recently due to ankle ligament damage.
The 22-year-old is entering the final season of his current Old Trafford contract, but Jose Mourinho could exercise the extra one-year option if he impresses in the new campaign.
Shaw only made 19 appearances for the Red Devils last season after struggling to break into Mourinho's first team. The United manager, however, did assure the defender he still had a future at Old Trafford.
One month after a 1-1 draw with Bournemouth, where Shaw came under heavy criticism from his manager, Mourinho said: 'Because of his age, physicality, intensity, aggression and ability going forward, he can be the best.
'But to be the best, you need to work hard and that's what he's trying to do.'