Hamburg only avoided relegation to the German second tier after an away-goals victory over Greuther Furth in last week's Bundesliga play-off, with skipper Van der Vaart one of many players struggling to find form throughout the season.
The 31-year-old came in for criticism from some sections of the club's support during the campaign, and has been linked with a switch to Besiktas.
However, Van der Vaart has no intention of leaving the Imtech Arena, instead setting his sights on an improved showing next term - both individually and collectively.
"Of course, I've played really bad football in the last few months," he told Bild. "It's obvious that they (the fans) doubted me. I would love to prove it (his ability) in the Hamburg shirt.
"I think we all, players, staff and fans have heard and felt the loud shot across the bow. The entire club must now make the right decisions.
"I would like to be at my club, Hamburg, in the coming season. I love this club and would like to stay.
"I haven't spoken with anyone from this club (Besiktas).
"Besiktas has been in contact with my agent in Holland, but I do not know if they have made an offer."
