Le Parisien say Jurgen Klopp is considering a potential reunion with the striker at Anfield having previously coached him at the Westfalenstadion.
The Reds’ place in the Champions League next season strengthens their hand and the Gabon forward has made noises he would be willing to leave Dortmund.
The 28-year-old was set to join Paris Saint-Germain but the move fell through. He is likely to cost £60million.
Aubameyang scored 42 goals for club and country last season and is seen as one of the most feared strikers in Europe.
Dortmund endured a troubled campaign last year as they finished a distant third, 18 points behind rivals and title winners Bayern Munich.