Modric has been linked with a move to the Spanish capital all summer after Jose Mourinho pinpointed the midfielder as his No.1 transfer target.
The Croatian was close to joining Chelsea last summer and has also been linked with Manchester United, and Van der Vaart says that Modric is upset over the situation, but he expects a resolution this week.
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"I went to Luka's house and spoke to him after training," Van der Vaart told AS. "I told him what happened to me when I wanted to sign for Real [from Hamburg].
"I've been one of the closest people to Modric in the dressing room and I feel for him. It is a difficult situation.
"The chairman is angry, but Luka is very upset with what is happening. I think everything will be fixed in three or four days."
The Netherlands midfielder also said that he knows how big the lure of Los Blancos can be, having previously played for them - and has stated that they are the biggest team in the world.
"You can't compare Real Madrid with other teams because they are the biggest team in the world," he told Sky Sports News.
"It was really an honour that I played there and I'm still really thankful.
"I think every player wants to play there."
Modric reportedly angered chairman Daniel Levy after he refused to fly out with the rest of the Spurs squad for their pre-season tour of USA.
It is expected that he will face disciplinary action from the club irrespective of the outcome of Real Madrid’s pursuit of his signature.