United are chasing a holding midfielder despite signing Nemanja Matic from Chelsea in the summer.
Monaco’s Fabinho remains on their radar but Weigl, the Independent say, could make the move instead.
Mourinho has reportedly long harboured hopes of luring the 22-year-old to Old Trafford.
And, while a swap deal involving Mkhitaryan is unlikely, United are banking on his return to smoothen negotiations.
Meanwhile, Mourinho has admitted the player could be involved in tomorrow’s Carabao Cup clash with Bristol City.
Mourinho not happy with Henrikh Mkhitaryan's Man Utd displays
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Manchester United admire Borussia Dortmund star Julian Weigl
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"He can. I am making a few changes for the match, not many, because Bristol is one of the best teams in the Championship and for me now the Championship is not the Championship of five or 10 years ago,” he said.
“The Championship is now high-quality teams with lots of players that could be playing in the Premier League easily.
“So we need to take the game really seriously. But I am going to make a few changes and it's possible Mhiki is involved.
"At the moment we are playing (Juan) Mata, (Marcus) Rashford, (Jesse) Lingard or (Anthony) Martial, (Romelu) Lukaku and the bench has been Ibra and one of the other ones - Martial or Rashford.
"There is no space for everybody because you need balance on the bench too."