The Netherlands midfielder, who made two appearances for his country in their run to the semi-finals of the World Cup, has been heavily linked with a move away from the Rotterdam club.
Portuguese side Porto are among those thought to have been interested in the 23-year-old, along with Premier League sides Manchester United and Southampton.
Coach Fred Rutten has seen a number of key players head through the exit door in the transfer window, with Graziano Pelle, Stefan de Vrij, Bruno Martins Indi and Daryl Janmaat all departing for pastures new.
But Clasie has decided not to join the exodus and is confident he can continue to develop in the Eredivisie.
"I feel I can improve even more at Feyenoord," Clasie told Feyenoord's official website.
"The club expresses a lot of confidence me while I have a lot of confidence in the future of the club.
"I base this confidence both on the discussions I've had with the club and what I see every day on the field.
"I have a feeling the team can really start growing and I would like to be a part of it."