The former Barcelona forward arrived at Old Trafford from the Emirates in the January transfer window. As a part of the deal, the Red Devils allowed Henrikh Mkhitaryan move in the opposite direction.
Since joining the 20-time English champions, Mourinho has deployed Sanchez on the left side of United's attack. Prior to his arrival, Anthony Martial was preferred ahead of Marcus Rashford by the Portuguese tactician. Sanchez's addition to the squad has seen Martial being deployed on the right. The Frenchman is yet to find the back of the net.
The South American star struggled to replicate last season's form for the Gunners in the first half of the ongoing campaign. He has scored once and registered two assists in six appearances in all competitions for the Manchester outfit.
Winterburn has backed Sanchez to be a success at United, but has advised their supporters to be patient before they see the best of the 29-year-old forward.
"He will make his mark eventually at Manchester United that is for sure," Winterburn told Sky Sports.
"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."