United have not scored in three of those games, losing at Tottenham and Newcastle before drawing 0-0 against Sevilla on Thursday, with Mourinho deploying Sanchez primarily on the left of United's attack.
Anthony Martial had previously staked his claim for that role but he has not scored since netting the winner in a 1-0 victory away at Burnley in the game prior to Sanchez's arrival, as he has struggled to adapt to playing on the right.
Winterburn believes Sanchez would be best utilised at United in a central attacking role where he can offer more support to Romelu Lukaku.
"I actually believe personally that this season Sanchez has not been at the same high level that he was at last season. He has just had a slight [dip] in form.
"He has now moved to a new club. How will Manchester United use Sanchez best within the dynamics of their set-up?
"I just wonder eventually whether Sanchez will come in and play off the central striker in Lukaku. I could see that working very, very well for them.
"Then you can use Martial or Rashford down one of your wings as well. I think that might start to excite some of the Manchester United supporters. It is a way of getting another creative player into your team.
"He is going to be a huge success but it is going to take him a little bit of time to settle in to the different styles of Arsene Wenger and Jose Mourinho."