Chiefs coach Romeo Crennel told the team of his decision before Monday's practice.
The race to back up Matt Cassel had been one of the few open contests for Kansas City during training camp. Quinn signed as a free agent in the offseason, and Stanzi was No. 3 a year ago.
Tight end Kevin Boss missed practice for what Crennel called personal reasons. Defensive backs Jalil Brown, Kendrick Lewis and Brandon Flowers were among numerous players who did not participate because of various injuries.
The Chiefs wrap up their preseason Thursday night at Green Bay.