Posey was waived by the Ravens on Friday.
Posey brought in both of his targets for 31 yards and a touchdown in the Ravens' 27-10 preseason win over the Dolphins on Saturday.
Posey will be released by the Jets, Seth Walder of the New York Daily News reports.
DeVier Posey is the leading candidate for the Texans slot job.
Coming off a 2012 Achilles' tear, Posey had just 15 catches for 155 yards and no scores in 14 games last season. He'll improve on that this year, but won't get on the fantasy radar while playing behind Andre Johnson and DeAndre Hopkins on a team that wants to defend and run the ball to win. The third receiver job isn't expected to be a big one for new coach Bill O'Brien, who projects to run plenty of "12" formations.
Texans WR DeVier Posey suffered a high-ankle sprain in Houston's Week 15 loss to the Colts.
With only two weeks to go, it's likely a season-ending injury for the second-year pro. Posey was held without a catch before going down against Houston, and has just 15 grabs on the year. Posey is not a must-hold in Dynasty leagues, but he's not a must-drop, either.
DeVier Posey caught just one pass for five yards in Houston's Week 12 loss to the Jaguars.
Posey's fourth-quarter catch was his only target, while he ceded snaps to Keshawn Martin. Posey isn't on the WR5 radar for a team plumbing new weekly depths.
DeVier Posey caught three balls for 34 yards in the Texans' Week 10 loss to the Cardinals.
Posey has taken over as the Texans' third receiver behind Andre Johnson and DeAndre Hopkins. Outside of Dynasty and 20-team leagues, the 2012 third-round pick out of Ohio State carries no fantasy appeal. Posey would need a Johnson or Hopkins injury to be worth consideration in standard settings.
DeVier Posey had three catches for 23 yards in Week 9 against the Colts.
He was targeted four times in the passing game. Posey has replaced Keshawn Martin as the No. 3 receiver, but doesn't have a defined role in the offense. He can continue to be ignored in fantasy leagues.
DeVier Posey caught a 42-yard pass in Houston's Week 7 loss to the Chiefs.
Posey's sixth catch of the season more than doubled his 2013 yardage total. There's no reason to believe his role will increase any time soon.
Texans coach Gary Kubiak said Friday WR DeVier Posey is at least "a few weeks away" from being a game-day contributor.
Coming off a late-season 2012 Achilles' tear, Posey was among the Texans' Week 1 inactives. He'll stay that way until he regains "confidence and what he's doing in physical shape." When Posey does return, he could overtake Keshawn Martin in three-receiver sets with Nuk Hopkins and Andre Johnson.