The Daily Star says United have been tracking him for 18 months and had an £18m bid rejected when Sir Alex Ferguson was in charge.
But Moyes has told United bosses he doesn't want another out-and-out striker.
A club source said: "Lewandowski has been a target but the new manager can't see where he would fit into the team. Other areas of the squad need strengthening and so the manager has turned his back on Lewandowski so the manager has turned his back on Lewandowski once and for all."
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