The opening game would replace the home-and-home series scheduled for 2013 and 2014 for the two teams. They will not play in 2014.
The news was first reported by the Fort Worth Star-Telegram.
LSU beat Oregon in the Cowboys Stadium Classic in 2011, and TCU started the 2010 season with a victory against Oregon State.
The Tigers had a nice crowd when they played in the Arlington stadium, which is about 20 miles from TCU's campus.