According to Amalia Fra of AS, the self-proclaimed Special One could move for the former Barcelona talent after a year in the Bundesliga. The Red Devils boss sees Bartra as a worthy addition after the signing of Victor Lindelof in June.
Italian journalist Tancredi Palmeri has fuelled rumours by announcing United are already in discussion to potentially buy the centre-back:
The Spain international departed Barca last term after a lack of opportunities under Luis Enrique at the Camp Nou.
The 26-year-old found a new home in Dortmund and appeared 26 times for the team in the Bundesliga and UEFA Champions League, per WhoScored.com.
The interest from United is strange considering the purchase of Lindelof and the presence of Eric Bailly, Chris Smalling and Phil Jones.
Bailly has quickly become a fan favourite at Old Trafford, and his performances helped United win two major trophies in his first season.
Here is Bartra in action:
In other news, United have completed the capture of Chelsea youth product Di'Shon Bernard as they refresh their academy stock.
United confirmed the news on their official website as they added 10 youngsters to the club.
Defender Bernard is considered a bright prospect at 16 years old and will now follow in the footsteps of United's young players as they battle to become top professionals.
United were strong in defence last season, but injuries tested Mourinho's options deep into the campaign.
Smalling and Jones have both consistently suffered with injury, forcing the pair to miss out on numerous games since the manager's arrival last summer.
Bernard could develop into a useful squad player within a couple of seasons, and Mourinho has proved he will give youth a chance after backing Marcus Rashford and Jesse Lingard during his tenure.