The newspaper said Delhomme, 36, got the nod over Jeff Garcia after both participated in workouts Tuesday.
The Texans (8-3) remain two games ahead of Tennessee atop the AFC South.
Delhomme's last experience came with the Cleveland Browns, for whom he played four games in 2010. He has thrown for 20,764 yards with 125 touchdowns and 101 interceptions over 10 NFL seasons.
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