The Texans announced the move Tuesday, a little more than a month after signing Brock Osweiler to a four-year, $72 million contract.
Hoyer met with the Jets on Tuesday, a league source told ESPN's Rich Cimini.
Fitzpatrick remains the Jets' No. 1 priority at quarterback, a league source told Cimini. The meeting with Hoyer is a get-acquainted visit, similar to Robert Griffin III's visit last month at the outset of free agency.
Hoyer signed a two-year contract before last season, but his five-turnover debacle in a 30-0 playoff loss to the Kansas City Chiefs suggested his days in Houston were numbered.
Hoyer was benched in the season opener and the Texans started Ryan Mallett for four games. But Mallett won just one of those games, and soon Hoyer was starting again. Mallett was released after missing a team flight. The Texans had to start both T.J. Yates and Brandon Weeden late in the season when Hoyer missed three games because he received two concussions in less than a month.
Osweiler agreed to leave the Broncos when free agency began even though he was the presumed replacement for the retired Peyton Manning.
Houston also released quarterback B.J. Daniels on Tuesday.
Information from The Associated Press was used in this report.