The Armenian started this season in fine form for Manchester United, registering five assists in his opening three Premier League games, but he has failed to add to that tally since August.
Mkhitaryan has subsequently been left out of the starting lineup for United's last five matches across all competitions, falling behind the likes of Anthony Martial, Marcus Rashford and fit-again Zlatan Ibrahimovic in Jose Mourinho's plans.
The Daily Star reports that Dortmund are hopeful of enticing the 28-year-old back to the Westfalenstadion while he is out of favour in a bid to improve their own fortunes.
Dortmund are winless in their last 10 league and Champions League matches, a run of form which has seen them slide down to sixth in the Bundesliga table and 10 points adrift of leaders Bayern Munich.
Mkhitaryan spent three years at Dortmund before joining United, scoring 41 goals in 140 appearances for the club.