Portuguese newspaper A Bola carries reports from Germany that claim Jurgen Klopp is looking to bring Kagawa back to the Bundesliga. And last year's Champions League finalists may be offered the Japan international as part of a deal for United target Subotic.
The Serbian international defender has been a long-term target for the Old Trafford club, with Moyes reportedly tracking him over the summer.
It could just be a case of putting two and two together, but the report claims United would welcome the interest in Kagawa if it allows them to secure their top transfer target in the January window.
The former-Dortmund star has failed to nail down a place under Moyes, and was replaced after just 45 minutes against West Brom after he was handed a rare start.
Reports had linked him with a move to La Liga - Atletico Madrid were mentioned as potential suitors - but Kagawa would likely favour a return to his former club, although he insists he's ready to fight for his place at Old Trafford.
Subotic, 24, is a key piece of Klopp's Dortmund side, helping the club to two Bundesliga titles and a Champions League final in the past three seasons.
United have been linked with several centre-backs over the past 12 months as Rio Ferdinand and Nemanja Vidic near the twilight of their careers, including Porto's Eliaquim Mangala.