Anderson has just won a first cap with England this past week.
Former United scout Mick Brown, speaking to Football Insider, revealed: "Man United have been looking at Anderson.
“He’s done a tremendous job at Nottingham Forest and then he’s come into the England side and turned in a man-of-the-match performance. United see him as exactly the type of midfielder they would like to bring in.
“He gets up and down the park, he’s confident and secure in possession of the ball, and he’s not afraid to put in a tackle, which is something they need.
“Anderson would solve, or certainly help with, a lot of the issues they’ve had under (Ruben) Amorim.
“Everybody knows they wanted a midfielder in the summer, but they couldn’t find the right one who was available at the price they wanted.”