The 25-year-old is Lokomotiv Moscow's top goalscorer this season.
The 25-year-old - who currently plays for Russian Premier League side Lokomotiv Moscow - is also attracting interest from Chelsea, Everton and Newcastle United, The Guardian claims, and could move for around £15m.
The Guardian suggests that with his wife based in Manchester, Niasse wishes to make the switch to England, having played in Russia since 2014.
Due to Niasse's personal circumstances, it may appear that Louis van Gaal's side are the ones that will be leading the charge for his signature. And while Aston Villa's plight means that they need the striker more than any of the other teams plotting a move, United have been disappointing on many occasions this season, and certainly need more options in attack if they wish to earn a place in the top four.
Despite beating Swansea at the weekend, the Red Devils had previously endured an eight-match winless run, during which their methodical style was questioned once again.
It was often the pace and trickery of Anthony Martial that provided United fans with brief glimpses of optimism during the run, and with Niasse - who has scored eight goals in the league this season - offering many similar attributes to the Frenchman, United may decide that they need to engineer a move for the Senegal international.
However, with plenty of their Premier League rivals also weighing up a move, United may have to part with a considerable amount of money to get a deal across the line.