BILD says Lewandowski is set to accept an offer of £20.5million in wages from Manchester United to join the club in the summer.
United already have the best attack in the top-flight with 48 goals from 19 games but Ferguson, who watched Lewandowski when he played Manchester City at the Etihad earlier this season, wants the most potent strike force in Europe.
He believes pairing Lewandowski with Robin van Persie - and Wayne Rooney operating just behind - would give him that. The manager is also keen to re-united him with Shinji Kagawa, who formed a successful partnership before joining in the summer.
Lewandowski has scored 40 league goals in 83 games for the side and is in fearsome form, netting braces in each of his last three games for Dortmund.