The Jets chose not to tender Bostick, making him an unrestricted free agent, the New York Post reports.
The lowest restricted free-agent tender still costs $1.8 million, which is significantly more than the type of near minimum contract Bostick will likely receive. He caught only eight passes in 16 games last season, serving mostly as the No. 2 or 3 tight end. Regardless of where he lands, the 27-year-old likely will have to fight for a roster spot in training camp.