The veteran had been on the PUP list with a calf strain so far during training camp.
Wilson also reported Houston has cut WR Chad Beebe as they trim their roster.
Teams have until Tuesday afternoon to cut from 90 players to 85.
Jenkins, 28, is a former third-round pick of the Jets back in 2016. He played out the final year of his four-year, $3.12 million contract before returning to New York on a one-year, $5 million deal.
Jenkins then signed a two-year deal with the Texans in 2021 while testing the free-agent market.
In 2021, Jenkins appeared in 11 games for the Texans and recorded 20 total tackles, four tackles for loss and 2.5 sacks.