But later in the day, King said he would redshirt this season, giving him "the best chance to develop as a player, earn my degree and set me up for the best success in the future."
Cougars wide receiver Keith Corbin will also sit out this season and return in 2020.
Tulane rallied from a 21-point deficit to beat the Cougars 38-31 on Thursday night.
With just seconds left to play and the score tied at 31, Tulane's Jalen McCleskey made a catch in between two Cougar defenders over the middle of the field, then broke a tackle and into the end zone for the win.
King threw for 229 yards and two touchdowns, and ran for 116 yards and another touchdown for Houston (1-3, 0-1).