Dembele missed training without permission on Thursday, with Dortmund head coach Peter Bosz telling a news conference the club had been unable to contact Dembele.
Speculation that a move to Barcelona was imminent soon mounted before BVB issued a statement saying a bid had been lodged by the Catalan giants but it did not meet their valuation for a player they signed from Rennes for €15m last year.
The statement read: “Borussia Dortmund has held talks with the Catalan football club FC Barcelona regarding the possible transfer of the BVB player Ousmane Dembele to FC Barcelona.
“During this meeting, the representatives of FC Barcelona submitted a bid which did not match the player’s extraordinary footballing ability or value to the club, nor the present economic market situation of the European transfer market. BVB therefore rejected this offer.
“As there is no other offer from FC Barcelona to date, there is currently no transfer of the player to FC Barcelona and this is not currently likely.”
The 20-year-old has been touted as a target for Barca since Neymar completed his world-record €222million switch to Paris Saint-Germain last week.
Dembele scored 10 goals and supplied 21 assists in 49 games for Dortmund in his debut season with the club.
Earlier this week, chief executive Hans-Joachim Watzke said a fee of €100m for the player was “in every case, not enough” and the Bundesliga club’s asking price is reported to lie closer to €135m.