Mourinho publicly criticised Shaw after Saturday's FA Cup win over Brighton. And recent reports have suggested Shaw could look to leave the club in the summer.
But former Chelsea assistant coach Wilkins believes the Portuguese is trying to goad Shaw into proving him wrong.
"He is looking for a reaction from Luke," said Wilkins.
"I feel for Luke a little bit because when he was at Southampton he looked an outstanding prospect at left back and it was a good move for him to move to Old Trafford.
"But I've said on numerous occasions - when you go to Old Trafford, it's not only what you can do with the ball, you've got to have the mentality of a winner as well and perhaps Jose is not quite seeing that in Luke at this moment in time."