The two schools are negotiating to play a game at Cowboys Stadium in Arlington, Texas, in 2011. According to sources, the contest could take place on Thanksgiving weekend and it would be broadcast by ESPN.
The Cougars, who are bolting the Mountain West Conference, begin their first season as an independent next fall. They are set to play 12 games, but they can add a 13th due to an NCAA provision that provides teams that play at Hawaii that option.
BYU has a bye on Nov. 26, which is Thanksgiving weekend. The Cougars begin an eight-year contract with ESPN beginning this fall.
TCU, which is going into its final season as a member of the Mountain West Conference, is looking to fill holes in its schedule that features two only non-conference games, against Baylor and Southern Methodist.
BYU played at Cowboys Stadium in Arlington in 2009, upsetting Oklahoma. Last September TCU defeated Oregon State at Cowboys Stadium.
When word got out about BYU going independent last August, Horned Frog coach Gary Patterson said he wouldn't consider playing the Cougars in the future.
TCU announced in November it is heading to the Big East Conference in 2012.