Foot Mercato says United are interested in v Zagadou.
The 23-year-old will officially become a free agent when his contract with Dortmund ends next Thursday.
However, newly-appointed Nice manager Lucien Favre wants to reuinite with Zagadou after their time together in Germany and is set to offer United competition.
The centre-back, who began his professional career with Paris Saint-Germain, told beIN Sport last month when asked about his future: "A return to Ligue 1? Of course. I left to go abroad very young, so it would be good for me to go back to France. I'm not putting up any barriers to a return."