I'll be delighted if Bellore is back on the roster next year. Bellore was one of the Jets' best three special teamers last year and the Jets have already addressed the other two, by franchising kicker Nick Folk and re-signing Ellis Lankster.
Any other team could sign Bellore to an offer sheet by May 2nd, which the Jets would then have the option to match (with five days to decide). As he was undrafted, there is no compensation involved. He could agree to a long-term deal with the Jets in the meantime, but if he simply remains on the tender he'll be under contract for this year at $1.431m and then an unrestricted free agent this time next year.
Bellore, still only 24, has only played sparingly on defense (18 snaps) over the course of his three seasons in the league, but has made some promising plays in preseason. 44 of his 46 career tackles were on special teams. Incidentally, I think the tackle total in the above tweet is a typo because he only had 17 total tackles last year, according to NFL.com.