The development comes one day after Smith said during a news conference that his time with the team was not over and that he plans to return after a leave of absence.
Smith expects to take a year away to assist his wife Tiffany, who was diagnosed with breast cancer in September and has been receiving treatment in Arizona.
While the Texans are looking to find a new general manager, Smith will maintain his other role as executive vice president of football operations. He is under contract through the 2020 season.
"If (the Texans) hire a GM and have a guy that runs the personnel, then we'll do that," Smith said. "Again, it's a fluid process, but I am absolutely intent on coming back. I will maintain at least the executive vice president title. And if (owner Bob) McNair feels like he wants to hire a general manager, then he will hire a general manager, and that will be just fine. "
Smith has worked for the Texans since 2006, when he became the league's youngest general manager at 36 years old.
Having a general manager who can work with coach Bill O'Brien is essential after the differences he has had with Smith over the last four years. There have been local and national media reports about Smith and O'Brien having a relationship that reached a boiling point during a 4-12 season.