The Bundesliga giants are looking to fine tune their squad and have set their sights on the Dutch attacker, who has refused to commit his future to the Premier League club
The German newspaper claims the Gelsenkirchen-based club have been locked in talks with Van Der Vaart's agent as they wish to pair the 29-year-old with prolific striker Klaas-Jan Huntelaar.
Van der Vaart was close to joining Schalke in 2010, but a move failed to materialise as he instead left Real Madrid for Tottenham
But when questioned about the reports, the former Hamburg player told Bild that he was focusing on this summer's European Championships.
"I do not want to say anything on this matter. Right now I am focused on Euro 2012."
Meanwhile, it is reported that Schalke are also pondering the possibility of signing Chelsea attacker Salomon Kalou.
The Cote d'Ivoire international, who has been at Chelsea since 2006, has been a bit-part player at Stamford Bridge. His contract expires this summer, so no release fee would be required to acquire his services.