Kyle Rudolph's sizable contract (4 years, 36 million dollars) that he signed last year simply counts too much against the salary cap. That, plus Irv Smith looks to be ready to be the unquestioned TE1 on that team.
Kyle Rudolph will have absolutely no problems finding a starting TE job elsewhere, although I doubt he'll command that high of a salary (and I hope I'm proven dead wrong). The NE Patriots would seem like a logical destination, seeing how they haven't found an adequate replacement for Rob Gronkowski (neither Izzo nor LaCosse were particularly effective).