A proposal to separate the roles of chairman and CEO will be voted on at the company's annual shareholder meeting. Hastings, who co-founded the company, holds both titles.
Supporters to separate the roles include Calpers, the massive California public pension fund, and Scott M. Stringer, New York City's comptroller and the overseer of the city's pension funds.
"A board that ignores its shareholders is a house of cards," Stringer told The New York Times, referring to Netflix's popular original series.
In recent years, many U.S. companies have separated the chairman and CEO positions out of the belief that if the CEO is also chairman of the board, the board won't be able to evaluate his decisions and performance objectively.
In the case of Netflix, some of Hastings ideas have hurt the company and its stock.
In July 2011, Netflix announced that it would cut DVD rental prices but charge for its steaming service, which had been free.
For the group that enjoyed streaming, the move resulted in a cost increase of up to 60%. The move led to customer backlash, with cancellations, falling subscriber growth and a rapid decline in the company's stock price. Netflix admitted its mistake, but kept its policy in place.