The Dutchman joined Hamburg from Tottenham in August 2012, but despite a strong campaign, could not lead Thorsten Fink's side to a European spot.
The Imetch Arena outfit finished seventh in the Bundesliga last term, and Van der Vaart is hoping to move further up the table in 2013-14.
"The goal is the Europa League," he told Bild. "Personally, I want to be important to the team. Looking back on last season, I believe I had a good year. I was satisfied, but I scored too few goals."
The 30-year-old is aiming to force his way into Netherlands' boss Louis van Gaal's plans for the World Cup in Brazil, and thinks an impressive second season with Hamburg could allow him to do so.
"Van Gaal is an honest coach. Everybody has the same chance under him," he added.
"If I play a good year, I have a good chance of being part of the World Cup squad. It would be a dream to take part in it once more."