According to German newspaper Bild (h/t Samuel Lovett of The Independent), BVB CEO Hans-Joachim Watzke has set the figure as they prepare for a flood of interest in the world-class attacker. Dortmund will listen to offers which they believe reflect Aubameyang's true market value.
"We will listen to it when a club is willing to show its appreciation for Aubameyang in a financial way as well," Watzke said, per Bild. "If an official bid were to reach more than £63 million, it would have to be reported as a necessary to proceed. This has not happened so far."
Aubameyang has hit 85 goals from 125 appearances for Dortmund, per Lovett, and has grown into one of the world's elite goal poachers.
Here is the player in action:
In other Reds news, Liverpool are interested in Napoli powerhouse Kalidou Koulibaly as they seek to strengthen their defence in the summer after signing Mohamed Salah from Roma on Thursday, per the Liverpool Echo.
Agent Bruno Satin said:
"Important players can receive offers, but at the moment he's a Napoli player and they can also reject them. Every day you can read about interested clubs, in terms of rumours you in Italy are top of the world. It's nonsense, and you don't only do it with Kalidou. There's a healthy working relationship with Napoli. Chelsea and Liverpool? I always talk with these kind of clubs, but about all of my clients, not just Kalidou. I do my job; we're in the transfer window."
The 26-year-old featured in 36 games in Serie A and the UEFA Champions League last term, according to WhoScored.com.
Aubameyang and Koulibaly would be huge assets for Klopp as the Reds attempt to navigate their way through European competition after an absence.
Liverpool are desperate to strengthen their defence in the coming weeks, and they were often exposed in Premier League matches last season, only saved by their scoring prowess.
Aubameyang would potentially be Liverpool's biggest signing in history, and his arrival could spell the end of Daniel Sturridge's time on Merseyside.