It has been widely suggested that Barcelona have met Dortmund's valuation of Dembele, which is said to be in the region of £138m, and that a deal would be announced imminently.
However, according to Eurosport, Dortmund have played down speculation over a possible transfer of a player who has only spent a year at the Bundesliga giants.
A spokesman is said to have stated: "We have set Barcelona a deadline, and either something will happen or it won't."
During his first campaign at Dortmund, 20-year-old Dembele - who still has four years remaining on his current deal - contributed 10 goals in 49 appearances in all competitions.
Barcelona have over £200m to spend in the transfer market after the sale of Neymar to Paris Saint-Germain.