The identity of Barca's replacement for Neymar, who joined Paris Saint-Germain for a world-record fee of $A331 million earlier this month, is yet to be determined, with Dembele and Liverpool's Philippe Coutinho believed to be the Catalan giant's preferred targets.
Dortmund told the German stock exchange last week that they had rejected a $A150 million bid from Barca for Dembele, who only moved to Signal Iduna Park from Rennes in July 2016.
The 20-year-old French forward has been indefinitely excluded from selection contention after missing a training session without permission.
Liverpool's owners, meanwhile, released a statement on Saturday (AEST) insisting it will not consider any offers for Coutinho, an announcement that was swiftly followed by reports the Brazil international had submitted a transfer request.
It remains to be seen if Ernesto Valverde's Liga powerhouse will succeed in securing the services of either player before the transfer window shuts on 31 August.
Watzke, though, may have sought to force Barca's hand with his latest remarks regarding Dembele.
"The time horizon is enough for two games," he told Kicker when asked for an update on the situation.
Dortmund is away to Wolfsburg in its opening game of the new Bundesliga season on Sunday (AEST), followed by a home match against Hertha Berlin a week later.