Modric has been at the centre of one of the transfer sagas of the summer, with Chelsea having seen two bids rejected for the Croatia playmaker.
The Blues have been pondering whether to make a third attempt in the coming days, with reports claiming they will test Spurs' resolve with a £30million offer.
Tottenham chairman Daniel Levy has insisted Modric is not for sale at any price, but the player himself wants to move to Chelsea and has been angered by his current employers' stance.
Van der Vaart knows Modric has been upset by Spurs' refusal to negotiate with their London rivals but expects the 25-year-old to give his all when the transfer window closes in three weeks' time.
"I'm really happy that he's going to stay because he's an important player for us," Van der Vaart told Sky Sports News. "Almost every day we ask him to stay and say, 'Have a great season - then you can go!'
"The chairman always said he's going to stay, no questions about it.
"I understand he was a little bit disappointed, but in a few weeks he's going to be happy again."
Meanwhile, Tottenham look set to fail in their latest bid to sign Real Madrid midfielder Diarra.
Spurs reportedly held talks with Real with the aim of landing the 26-year-old, but his wage demands appear likely to scupper any deal.
Manager Harry Redknapp signed Diarra for Portsmouth in January 2008 and has made previous efforts to bring him to White Hart Lane.
Redknapp has also long been pursuing West Ham's Scott Parker, but wages could also prove a problem in the case of the Football Writer's Player of the Year.
Tottenham are already well stocked in central midfield, although they reportedly will listen to offers for Jermaine Jenas and Wilson Palacios.