Left-back Shaw became ill after recovering from a slight groin tear so will need assessing before the Premier League match at Old Trafford.
Attacking midfielder Mkhitaryan is building up his fitness after a thigh complaint and could be in contention.
Mourinho said after United's 1-0 win against Zorya Luhansk: "Let's see [about injuries].
"But normally yes, normally we have almost everyone in a condition to play. Of course, Phil has a long-term injury."