The Houston Chronicle first reported the news.
On Wednesday, it was reported that Mumphery was expelled by Michigan State in the summer of 2016 after he was investigated for an alleged sexual assault.
Bullough has been suspended for the first four games of the 2017 season for violating the NFL's policy against performance-enhancing drugs.
Both players played primarily on special teams last season for the Texans. Bullough played 30 games for Houston in his first three NFL seasons and played in place of an injured Brian Cushing early last year.