Ferguson and assistant manager Mike Phelan watched Lewandowski in action for the German champions against Manchester City earlier this season, with Jurgen Klopp, the Dortmund coach, admitting that United are keen to sign the striker.
While Dortmund remain determined to keep Lewandowski, the club are equally keen to avoid him joining Bayern, who look set to deny Dortmund a hat-trick of titles this season.
Lewandowski said: "After the last game of the season, I will sit down with my advisors and discuss everything and we will see what's next.
"It's nice that other clubs are interested but I am getting annoyed by all the speculation. For now I just want to concentrate on doing my best for Dortmund and Poland."