An initial Barca offer was rejected by Dortmund with club bosses saying it was too low.
Barcelona are struggling to bring in a replacement for Neymar, given Liverpool also rejected a €100m [£90.4m] bid for Philippe Coutinho, despite the Brazil global handing in a transfer request by email on Friday.
However, with Dembele recently going AWOL from team training, deciding instead to remain in Paris in order to force a move to the Camp Nou through, with BVB manager Peter Bosz confirming that Dembele was not in training, during a press conference on Thursday.
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 a year ago.
"We will of course sanction this misconduct", Dortmund's sporting director Michael Zorc said in a statement. Chelsea must spend, spend, spend!
The 20-year-old France global was fined and suspended until Monday for missing Thursday's training, but the ban has been extended indefinitely. 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.
"Ousmane Dembele has the possibility to do individual training away from the group". "Whatever happens, happens. It's a hard situation".