The Texans added an important piece of their quarterback puzzle on Monday when Ryan Mallett signed a two-year contract worth $7 million.

But there's still a missing piece in Brian Hoyer.

Despite early-morning reports that Hoyer had agreed to a contract with the Texans, no deal was worked out because the New York Jets were making a late run.

Hoyer is expected to sign with the Texans on Tuesday, but the earliest he can do it is 3 p.m., when free agency starts and the annual feeding frenzy begins.

Signing Hoyer would allow the Texans to release or trade Ryan Fitzpatrick, a move that would clear an additional $3.25 million in salary-cap space.

The Jets are a possible destination for Fitzpatrick. Not only is their new general manager Mike Maccagnan familiar with him because he was the Texans' director of college scouting, but new offensive coordinator Chan Gailey was Fitzpatrick's head coach at Buffalo.

Coach Bill O'Brien wants competition for the starting job. Mallett was 1-1 as a starter last season, and Hoyer was 7-6 with Cleveland.

Hoyer can join a group of quarterbacks that includes Mallett, Tom Savage and possibly Case Keenum. The Texans want to bring back Keenum, a restricted free agent who was 2-0 as a starter at the end of last season.

Thaddeus Lewis, who was on the roster part of last season but didn't play, was released Monday.

If the Texans get Hoyer, it's because he wants to be reunited with O'Brien, his quarterbacks coach and offensive coordinator for three seasons (2009-11) at New England.

Mallett, 26, wanted to stay with the Texans and continue playing for O'Brien and quarterbacks coach George Godsey.

Mallett could have gotten more money from another team - presumably the Jets - according to a person familiar with the negotiations.

After his two starts, Mallett underwent season-ending surgery for a torn pectoral muscle. When making his decision, he knew he'd have a better chance of success playing for O'Brien and Godsey again.

Mallett knows the Texans' system because he also was in it during his three years at New England. If he wants to excel and sign a contract befitting a starting quarterback, his best chance was to stay with the Texans.

Mallett wasn't made available to the media, but his agent, J.R. Carroll, tweeted a quote from his client: "When I got to Houston, it felt like home, and when I entered the facility, everyone treated me as if I was family."