The 26-year-old Gabonese international has been linked with the Premier League pair in recent weeks and was absent as the Dortmund squad returning from their winter break on Tuesday.
A spokesman for the Bundesliga club since explained that Aubameyang missed the session ‘for personal reasons’ but rumours are rife about his future.
"We all hope he'll [Aubameyang] stay," said team-mate Matthias Ginter after the first training session in January.
"He's very important, on the pitch and off, for what he contributes to the group atmosphere."
Aubameyang is the Bundesliga top scorer with 18 goals to his name before Christmas and is under contract with Dortmund until 2020.
This development comes just 24 hours after chief executive Hans-Joachim Watzke was forced to address the speculation with the media.
He told Bild: "One must never make the mistake to believe that a club like BVB is dependent on a player. We are not dependent on anyone.
"When Robert Lewandowski left, we found [a solution] and he even has three more goals than Lewa.
"[The goal is that] our team stays together. We do not have as much money as the top stars in the Premiere League, but we have a lot of other things to offer - for example our players were able to celebrate Christmas.
"Last year around this time, many journalists wrote that our top players would be gone.
"Hummels was at Manchester United. Gundogan was with [Real] Madrid, Manchester or Barcelona. And where are they now? Still with us."
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