The requirement for constables and deputies to be British citizens could be removed if a proposition is approved.
Deputy Montfort Tadier said "great steps" had already been achieved in making Jersey a "more inclusive" and diverse community.
In 1994, non-British Jersey residents were allowed to vote in elections; in 2000, non-British nationals were able to serve on a Jersey jury, and in 2004, they were able to join the Jersey Police.
Tadier said the "primary concern" of an eligible candidate should be their skills and what they can offer to the public service - not if they can pass the nationality test asking "what colour a Beefeater's uniform is".
He said: "Most right-thinking people will probably tell you that they don’t place so much importance on characteristics such as race, nationality, sexual orientation, age or gender.
"When it comes to someone’s potential to do a job, it is what skills, experience and knowledge they have to offer that counts - this should also be the case for political office."
The proposal also requested the Privileges and Procedures Committee to bring forward any necessary legislative changes in time for the 2026 election.
The earliest opportunity for it to be debated will be Tuesday 22 October.