The deal will make Dortmund's goal machine the world's highest paid footballer
The club, formed only 10 years ago, are reportedly willing to offer the 27-year-old €50 million a year (almost £43 million) to move to the fledgling Chinese Super League.
Quanjian is also willing to pay Dortmund €80 million (close to £68 million) to buy the Gabonese captain out of the remaining three years of his contract at the Westfalenstadion.
This deal, which would see Aubameyang earning over £800,000 every week, would make him the world's highest paid footballer.
Aubameyang, considered to be one of the world's fastest footballers as well as one of the most lethal strikers in the game, has scored 37 goals in 44 games across all competitions for Dortmund this season.
Since joining BVB in 2013, he has scored 117 times in 187 games.
He was the first Gabonese to be named African Footballer of the Year in 2015.
Tianjin Quanjian, currently 10th in the Chinese Super League, are coached by 2006 World Cup-winning captain Fabio Cannavoro.