The 34-year-old Hildebrand, who joined as an emergency replacement to injured Ralf Faehrmann in 2011, has lost his starting spot halfway through the current season after his younger teammate fully recovered from his serious knee injury.
Schalke sports director Horst Heldt praised Hildebrand's contribution in the past seasons but said the club was now focused on the future.
"Our task with any contract decision is to look ahead. In this position (goalkeeper) we want a different setup and this is something we have told Timo," Heldt said.
A Germany reserve keeper at the 2006 World Cup, Hildebrand has also played for VfB Stuttgart, Valencia, Hoffenheim and Sporting Lisbon.
Schalke are through to the Champions League knockout stage where they will face Real Madrid in February.
(Reporting by Karolos Grohmann; editing by Amlan Chakraborty)
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