The 24-year old still has another year remaining on his contract at the Westfalenstadion, but he was reported to be looking for an exit, with UEFA Champions League winners Bayern Munich the Poland international's desired destination.
Watzke had recently stated his reluctance to allow Lewandowski to leave but he says that any interested teams will need to act quickly.
"There has been no general change on this. But the proposed time window for interested foreign clubs is not open for much longer," he told German newspaper Ruhr Nachrichten.
"It is a fact we need a severe certainty for our season plan.
"Robert Lewandowski has insisted on his wish to join Bayern Munich, therefore there is no real issue on him moving abroad.
"Borussia Dortmund has not handed any written allowance to Robert Lewandowski on a move to Bayern Munich. There is zero official correspondence existing."
Meanwhile, Arsenal are reported to be in the market for a striker and German international Lukas Podolski believes that Lewandowski would be a perfect signing for the Gunners.
He told Polska The Times: "He would fit ideally into our team, Arsenal."