ESPN's Adam Schefter reports that Smith is taking a leave to be with his wife, who was recently diagnosed with breast cancer.
According to a report from the Houston Chronicle's Aaron Wilson, the relationship between general manager Rick Smith and coach Bill O'Brien is "toxic" and "dysfunctional," which could lead to changes in Houston this offseason.
Smith and his wife, Tiffany, have three children.
However, McNair may feel inclined to choose between O'Brien and Smith if the team owner believes the longstanding issues between the two can not be resolved.
Smith has been the GM at Houston for 11 seasons now, and the Texans have gone 88-104 during his tenure. This was an extremely hard decision for me to make as I love this organization and every member of this team both on and off the field.More news: Rockies Sign Wade Davis
The McNairs want to move fast because the Texans need their new general manager and O'Brien to be on the same page because they'll have free agency (in March) and the draft (in April) to improve a team that plunged from first to worst in the AFC South this season.
O'Brien has one season remaining on a five-year deal he signed when he became the Texans' coach in 2014.
Smith released a statement on Sunday after the Texans' 22-13 Week 17 loss to the Indianapolis Colts.