Sky Italia (h/t TalkSport) reported the midfielder has turned down the opportunity to join the Nerazzurri, who have scouted him as they considered a loan approach.
Mkhitaryan's stock has plummeted at Old Trafford, and manager Jose Mourinho forced the player out of his squad after a series of poor displays.
However, the Armenian has slowly been reintroduced by the Special One, but Juan Mata's form has seen the Spaniard become the preferred choice as a No. 10 option.
The 28-year-old—who signed from Borussia Dortmund at the start of last season—has made 15 appearances in the Premier League this term, providing five assists.
Per Sky Italia, BVB are considering an approach for their former star, giving Mkhitaryan a route back to the Bundesliga.
However, separate reports said it was Mourinho who blocked the potential deal with Inter as he thwarted the intentions of his former club.
Jeremy Cross of the Daily Star reported the Italian club were ready to provide the player with a six-month loan deal, but the United boss will not entertain the idea. Inter reportedly offered Joao Mario as part of the loan, but Mourinho does not require the Portuguese midfielder.
In other United news, Spanish duo Mata and Ander Hererra have had their current deals extended by 12 months, alongside squad members Ashley Young and Daley Blind.
James Ducker of the Telegraph reported the four players had automatic extensions triggered by the Red Devils to tie them to the Theatre of Dreams. The move stops the group becoming free agents in the summer. Marouane Fellaini has failed to sign a new deal under Mourinho and can potentially exit on a free at the end of the season.
Securing the quartet will allow Mourinho to flex his options with clarity, and he can now sell them for a fee next summer if he chooses to cut them from his plans.
Young has made a triumphant return to the starting XI this term, claiming a full-back berth as the United coach rotated his defence.
Per Ducker, United could potentially lose Michael Carrick and Zlatan Ibrahimovic with Fellaini at the end of the season, freeing up sections of the wage bill for new additions.
United have suffered as they witness the rise of Manchester City this term, but the performance of the Red Devils suggests success is not far away.
The Old Trafford giants have lost only three matches in the Premier League this season and remain six points ahead of fifth-placed Tottenham Hotspur.