The 24-year-old has had an impressive spell at the Ligue 1 side this season which earned him a call-up to the England squad under former interim manager Lee Carsley who saw the potential in the young star.
According to the Telegraph, any move will have to wait until the summer, when he'll be available for free after his contract expires. Top clubs such as Tottenham and West Ham are said to be very interested and will certainly be keeping an eye on him for the remainder of the campaign before making a final decision on his future.
The midfielder told L'Equipe that leaving Old Trafford initially in 2020 was "very difficult" and that he would like to return one day if the opportunity occurs. With his contract set to expire a move back to United could be on the cards.
"It was a very difficult decision," he said. "In my heart, I wanted to leave, in my head, I was thinking of staying. But I had to follow my heart. I felt that I needed to take another step in my career.
"I felt that had I stayed, there wouldn’t be a lot of opportunities for me. Luis Campos (Lille's then sporting director) and Lille spoke about their project and I believed in it even more, that’s what convinced me to move - the faith Lille had in me.
"Do I imagine myself coming back one day? Obviously, it’s home. I would love to come back. But you never know in football. I just have to keep my feet on the ground, and keep playing, making the most of it. I can’t predict what will happen in the future."