Fernando Torres is returning to Atletico Madrid on loan until the end of the 2015-16 season.
Steve Clarke is hoping to keep Glenn Murray at Reading after his loan deal expired following the 2-1 win over Norwich.
Van der Vaart, along with a number of his team-mates, failed to sparkle as Hamburg only stayed up courtesy of winning the end of season promotion-relegation play-off.
31-year-old van der Vaart has been linked with his former Tottenham boss Harry Redknapp, now at Queens Park Rangers, and Turkish side Besiktas.
But van der Vaart insists he wants to stay at the Imtech Arena, where he has another 12 months left on his current deal.
Van der Vaart told Bild: "I am able to understand a top-earner and skipper of any club being criticised after such a disastrous campaign.
"I certainly had a weak second phase of the season. I am looking forward to having a much better campaign alongside my Hamburg team-mates.
"I am going to play for Hamburger SV in the new season. To make sure the supporters are getting the good Rafael and not the weak one from those last few months!"
One player who will not be alongside van der Vaart is Zhi-Gin Lam, who has joined Greuther Furth after the 23-year-old full-back agreed a three-year deal with the second division club.