Van der Vaart has been strongly linked with a return to his former club but the Bundesliga side's chairman, Carl-Edgar Jarchow, has admitted time is running out to convince Spurs to sell.
"There is not a lot of time - it is really up to Tottenham Hotspur," he told German news agency Deutsche Presse-Agentur.
"If we have a chance to sign him, we will do everything we can to make that happen."
That opportunity could present itself if Tottenham complete the signing of some of their own targets during what looks set to be another frantic final 48 hours of a summer transfer window at White Hart Lane.
Moussa Dembele was today on the brink of sealing a move from Fulham after Spurs triggered what was reportedly a £15 million release clause. New manager Andre Villas-Boas has also renewed the interest he showed while Chelsea boss in Shakhtar Donetsk forward Willian, who could fill the void left by the departure of Luka Modric.
Shakhtar chief executive Sergei Palkin claimed on Wednesday he had rejected a bid of just under £12m for the Brazilian and that Tottenham chairman Daniel Levy had also made an inquiry about two other players.
"Mr Levy, the chairman of Tottenham Hotspur FC, personally flew to Donetsk to negotiate over Willian," Palkin told his club's official website.
"But his latest offer was 15 million euros, which we, of course, did not accept.
"Levy, by the way, hinted that besides Willian, Villas-Boas was interested in Douglas Costa and Fernandinho, but he mentioned that just casually, without any specifics."
- Tottenham Hotspur