The N.C. Senate's Education Committee gave a favorable report on a bill earlier in the day. It will now head to the House.
No date has been set for when House debate will begin.
But some members of the Senate fear that eliminating the quotas, which require that a minimum number of seats be given to women and racial and political minorities, will lead to underrepresentation of key interest groups.
Under the present system, 12 of the 32 seats must be given to women and racial and political minorities -- four seats for each.
"Eliminating quotas might preclude, for example, the presence of Republicans on the BOG," said Sen. John Garwood, R-Alexander, a member of the committee.
Garwood's concerns stem from the nature of the BOG appointment process. Members serve staggered four-year terms, with new members appointed on odd-numbered years.
The proposed bill states members should be selected based on a knowledge of the needs of students with respect to their "economic, geographic, political, racial, sexual and ethnic diversity."
The bill was introduced in response to a lawsuit filed May 30 by former BOG member Walter Davis that aimed to eliminate the mandatory quotas for board seats.
But Sen. Jeanne Lucas, D-Durham, co-chairwoman of the committee, said the language of the new bill encourages legislators to keep the interests of minorities in mind. "People in the House and Senate will have to be diligent about making sure representation is geographically, politically and racially minded."