Gipson signed a three-year, $22.5 million deal with the Texans last offseason after previously playing the previous three seasons for the Jacksonville Jaguars.
While Gipson was brought in to replace Tyrann Mathieu, who left for the Kansas City Chiefs in free agency, injuries limited his performance in 2019.
Gipson started 14 games for the Texans, had three interceptions and was tied for fifth on the team in combined tackles.
A wrist injury plagued Gipson earlier in the season, while a back injury landed him on the injured reserve late in the season.
He was unavailable for the Texans' playoff run, which included a tough loss to the Chiefs in the AFC Divisional Round.
Chiefs tight end Travis Kelce torched the Texans for 10 catches, 134 receiving yards and three touchdowns in Gipson's absence.
A stated reason for signing Gipson was his ability to cover tight ends.
They signed veterans Eric Murray and Jaylen Watkins this offseason, but it's unclear if either of them would be a starter like Gipson.
Texans head coach and general manager Bill O'Brien spoke before the draft about needing to add depth at safety. The Texans drafted former Penn State cornerback John Reid, who can play some star safety, but they still need to address the position.
Free safety Justin Reid has been vocal about wanting the Texans to take a look at his brother, veteran safety Eric Reid, a former Pro Bowler who was released by the Carolina Panthers in March.