He is also expected to confirm the signing of Swedish superstar Zlatan Ibrahimovic on a free transfer once he returns from Euro 2016.
Now it seems Mourinho wants to add Armenian international Mkhitaryan to his squad as well before United embark on their summer tour of the Far East next month.
Dortmund have valued the 27-year-old at £30m, but United are confident of reaching a compromise with them after bidding close to the asking price.
Mkhitaryan, who scored 23 goals in the Bundesliga last season, has just 12 months of his current deal remaining at Dortmund.
He has refused to sign a new one after setting his heart on a move to Old Trafford, but Dortmund bosses remain determined to keep him.