Seferian-Jenkins, a second-round pick of the Tampa Bay Buccaneers in 2014, was waived last week after his second DUI arrest.
Seferian-Jenkins, 23, would join a super-sized Jets' receiving corps with 6-foot-5 Brandon Marshall and 6-4 Eric Decker. Blocking specialist Kellen Davis, who is 6-foot-7, is listed as the starting tight end on the last depth chart.
Seferian-Jenkins was drafted 38th overall, 11 spots before Jace Amaro went to the Jets. Amaro was released in September before final roster cuts.
In the first game without Seferian-Jenkins, Buccaneers tight end Cameron Brate caught two touchdown passes from quarterback Jameis Winston in Sunday's loss to the Rams.
Buccaneers coach Dirk Koetter said the release of Seferian-Jenkins was more complicated than it might appear on the surface.
"It is disappointing. Austin's a guy that we had high hopes for, was a second-round pick here a couple years back, fought through some injury issues, very talented individual," Koetter told SIRIUS/XM Radio.
"There's more to every story than meets the eye, sometimes there's more to it than I can say on the radio."