Texans head coach Bill O'Brien said they began throwing the idea around after Quarterback Deshaun Watson tore his ACL last week.
Kaepernick hasn't been signed since the end of last season when he became a lightning rod of controversy for kneeling during the national anthem to protest social injustice.
O'Brien said he and general manager Rick Smith discuss the roster and which players are available every day.
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"Oh, yeah. Everybody gets discussed. Is that a problem?" O'Brien said. "Isn't that the way most teams do it? People seem shocked by that."
O'Brien called Kaepernick a "good football player" but did not answer a question about whether the team would even sign him if O'Brien wanted him.
Just days ago, a league source said Texans owner Bob McNair would be deposed in a grievance Kaepernick filed accusing NFL owners of colluding to keep him from playing.
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O'Brien said right now he expects Tom Savage to be the starter for Sunday's game against the Rams.
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