Keenum started eight games for the Texans last year. The Abilene native threw for over 1,700 yards and nine touchdowns before being replaced by Matt Schaub for the last two games of the season.
This past offseason the Texans sent Schaub packing for Oakland, and signed Fitzpatrick as a free agent.
Houston at the time had four quarterbacks on the roster after drafting Tom Savage out of Pittsburgh in the fourth round of the NFL Draft back in May.
On Tuesday the Texans cut their number of quarterbacks down to three after releasing TJ Yates. Leaving just Fitzpatrick, Keenum and Savage on the Texans roster for mini-camp.