When asked what he is looking for in a new head coach, Watson said, "We just need a whole culture shift.
"We just need new energy. We just need discipline. We need structure. We need a leader so we can follow that leader as players. That's what we need."
The Texas fired head coach and general manager Bill O'Brien in October and have been led by interim head coach Romeo Crennel and interim general manager Jack Easterby since.
Houston, which during the season began interviewing head coach and general manager candidates not currently employed by teams, has begun requesting permission from teams to interview candidates. On Monday, ESPN's Adam Schefter reported the Texans are requesting permission to interview New England Patriots director of player personnel Nick Caserio for their open general manager job.
ESPN's Ed Werder reported that Houston has scheduled a three-hour window on Sunday for a video conference interview with Indianapolis Colts defensive coordinator Matt Eberflus for the head coach opening, a day after the Colts' playoff game against the Bills.
Watson said Monday that he talked to Texans CEO Cal McNair on Sunday to discuss the open roles, expressing interest in offensive coordinator Tim Kelly potentially returning next season after the quarterback's career-best season.
"We've all got to be on the same page," Watson said. "There's too many different minds, too many different ideas and too many people thinking they have this power, and it's not like that. We need someone that stands tall, and this is who we follow and this is the way it goes."