Barcelona and Real Madrid both want to sign Dembele this summer and the player is aware of their interest.
Should Dembele's move go through it would see Dortmund make a huge profit on a player who has only played 32 games for the club.
It emerged earlier today that Barcelona were closing in on an agreement with Dortmund and Dembele also missed training with the Bundesliga outfit, which pointed towards an imminent transfer.
Reports in Germany claim Dortmund have rejected a bid from the Spanish giants and there are rumours claiming he is on his way to Barcelona.
Barcelona have made no secret of their desire to land a replacement for Brazilian superstar Neymar, who joined PSG in a world-record deal last week.
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The German side released a statement on Thursday afternoon confirming they had turned down the offer because it did not reflect the player's "extraordinary footballing abilities" or the "present economic market".
"As there is no other offer from FC Barcelona until now, the transfer of Dembele to Barcelona isn't likely". "BVB therefore rejected this offer".
"I'm not a phenomenon, I'm just trying to be decisive for my team-mates, there are a lot of talented young people in football", a modest Dembele said last March.
The France global scored 10 goals in 49 appearances last season after joining Dortmund for £13m from Rennes and helped the club win the DFB-Pokal Cup. "We hope nothing bad has happened".