Arsenal were previously thought to be weighing up a move early in the winter transfer window, but have since cooled their interest.
It's reported that both Chelsea and United have had discussions regarding Soumare, but Lille won't make a decision before they play Paris St Germain on 26th January.
Lille have a crop of promising young players coming through their ranks at the moment, but Soumare is the only one expected to leave this month.
The 20-year-old is a box-to-box midfielder who has been likened to Paul Pogba in his playing style.
Pogba himself is currently out with a long term injury and will miss yet more of the season as he recovers from a recent surgery.
With Pogba rumoured to be looking to leave United in the summer, Soumare could be the ideal replacement.
Chelsea are keen to invest for the future as rumours regarding N'Golo Kante's future continue to surface and resurface.
Soumare has played 23 games this season, including six appearances in the Champions League.
The blooding of a young player at such a high level is indicative of how much Lille rely upon the Frenchman.
Soumare has two and a half years left on his current contract and is valued at around £20m.
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