The Blues are intent on signing a world-class striker this summer, with Diego Costa also set to leave Stamford Bridge.
Chelsea manager Antonio Conte likes Aubameyang and the 28-year-old is on his shortlist with Alvaro Morata of Real Madrid, Torino's Andrea Belotti and another current Premier League striker.
Dortmund will let Aubameyang go this summer for about £70m and he has told the club he wants to leave, with both AC Milan and Paris Saint-Germain already holding talks to sign him, and a move to Tianjin Quanjian collapsed last week.
Dortmund chief executive Hans-Joachim Watzke says they have not received any offers yet and warned interested clubs that they are running out of time.
We will wait a few more days but not long anymore," he said. "I would personally prefer if he stays, but there are a few clubs on this planet where he can obviously earn more."
Dortmund want Aubameyang's future to be sorted out by July24 when they leave for a training camp in Switzerland.
Aubameyang was the top-scorer in the Bundesliga last season with 31 goals in 32 games. He scored 40 times in all competitions.
