The 35-year-old has spent several days training with the Bhoys. The former Middlesbrough and Marseille star left Sunderland over the summer.
“Celtic has confirmed that Boudewijn Zenden will not be joining the club on a permanent basis after he spent several days training with the squad,” read a statement on the the club’s official website.
“The Hoops were delighted the Dutchman decided to train with the club for a short period but both parties have agreed not to take the move further following discussions.
“Everyone at Celtic would like to wish the player their sincere best wishes in his future career.”