The audition included kickers Neil Rackers, Shayne Graham and Justin Medlock, but none will replace Bullock, interim coach Wade Phillips said Wednesday.
"We're going to continue to go with Randy," Phillips said, according to the Texans' official website. "He certainly knows and we told him, and everybody else knows. He's got to get it done."
Rackers said earlier Wednesday that the Texans had informed him they were not ready yet to move on from Bullock.
"We all hit the ball really well, but they told us they were not ready to make a move at this point," Rackers told KRIV-TV in Houston.
The key phrase in Rackers' comment is "at this point."