Ongoing talks between Modric and the Spurs supremo eventually resulted in Levy making a public announcement, stating that under no condition will they sell their prized asset.
The club have rebuffed a £22 million bid from London rivals Chelsea, while Manchester United are still thought to hold an interest in the player, as well as Arsenal's Samir Nasri.
The Croatian international was required to report back for pre-season training on Thursday, with Van der Vaart revealing the 25-year-old looked slightly dejected after the move had been denied.
"He was happy to see us," Van der Vaart told Sky Sports News. "Maybe [he was] a little bit disappointed but I can understand him. It's not easy when a club wants to buy you.”
However, Van der Vaart provided cause for optimism, insisting that Modric will not let events affect his performances for Spurs.
"But I think he's happy here and he also told me that he likes to play with us again and train with us. So we're happy that he's staying."
Modric had affirmed his interest in joining Chelsea following the Blues' bid, but Van der Vaart was unforthcoming if these were still his intentions.
"I don't know. That's not what he told me. He loves to stay here and he loves to stay in London," he said.
"Also, I think next season we have a good chance to win against Chelsea."
Tottenham have been forced to tighten their grip on their key players and Van der Vaart reiterated that this must continue to be the club's stance if they want to compete at the top end of the Premier League.
"We want to be in the top four again and maybe more this year. So we have to keep good players.
"We had a great season last year and this one is new again. I think it's going to be harder, but we've all stayed and we're going to play a great season."
