Bryant did not immediately return phone calls to The Associated Press seeking comment late Saturday and early Sunday.
Investigators did not immediately release the name of the second victim.
Witnesses told sheriff's investigators that a gunman opened fire on the men around 3:30 p.m. Saturday, then fled in a pickup truck belonging to one of the victims, according to the Star-Telegram. The newspapers said a 25-year-old man was later taken into custody in Lancaster, southeast of Dallas, and that charges were expected.
Lancaster police did not immediately return calls for comment.
The motive for the shooting was unclear.
Kyle wrote the best-selling book, "American Sniper: The Autobiography of the Most Lethal Sniper in U.S. Military History," detailing his 150-plus kills of insurgents from 1999 to 2009.