It's considering opening the process to everyone who applies and meets the minimum education and residency requirements.
City officials say eliminating the exam would help boost minority hiring and save millions on test preparation.
Critics argue that exam steps -- like the background check and psychiatric exam -- help eliminate unqualified applicants.
"The written exam is always a good indicator of potential as far as literacy, potential as a far as measure of common sense in some scenarios they are put into and have to respond to during the testing process," said Mark Donahue, president, Fraternal Order of Police.
A final decision to eliminate the exam could be made later this week.
