If formally named president, Meyers would be the first woman to lead Jackson State.
Meyers and Brown will now attend a series of campus meetings, leading up to a final vote by the College Board.
Alcorn State has been without a permanent leader since George Ross stepped down in February to become president of Central Michigan University.
Former JSU President Ronald Mason left at the end of June to take over the Southern University System, based in Baton Rouge, La. Former professor Leslie McLemore has been interim president.