Nasdaq Inc.-listed companies could soon face new rules requiring most of them to diversify their boards or risk getting kicked off the exchange.

In a proposal submitted to the U.S. Securities and Exchange Commission on Dec. 1, the New York-based exchange giant asked for permission to roll out a series of listing requirements that would force the thousands of companies listed on its U.S. trading venues to begin publicly disclosing diversity statistics about their boards and to have at least one diverse director on their boards within two years of the proposed rule's introduction.

Companies listed on either Nasdaq's Global Select Market or Global Market would then be expected to have two diverse directors within four years of the SEC's approval, while companies on the Nasdaq Capital Market will have five years to add a second diverse board member.

At least one of the two directors will need to be someone who identifies as female or as either an underrepresented minority or member of the LGBTQ+ community, according to Nasdaq.

Any company that is "not in a position to meet the board composition objectives within the required time frames" will not be subject to delisting as long as they provide a public reason why they are not able to do so, Nasdaq said in a statement. Foreign and smaller companies listed on Nasdaq will be able to satisfy the requirement by having two female directors, the exchange said.

The move from Nasdaq comes amid a broader diversity push across Wall Street and corporate America. State Street Global Advisors Inc., one of the world's biggest asset managers, announced plans earlier this year that it will begin to ask the companies it invests in to detail their risks, goals and strategies related to racial and ethnic diversity in 2021. Goldman Sachs Group Inc. began underwriting initial public offerings only of companies that have at least one diverse member of their boards in 2020. The investment bank has announced plans to expand that requirement to two diverse board members in 2021. And, in September, California Gov. Gavin Newsom, a Democrat, expanded a law in the state that requires publicly traded companies headquartered in the state to have at least one director on their board that comes from a historically "underrepresented community."

"Our goal with this proposal is to provide a transparent framework for Nasdaq-listed companies to present their board composition and diversity philosophy effectively to all stakeholders," Nasdaq President and CEO Adena Friedman said in a statement. "We believe this listing rule is one step in a broader journey to achieve inclusive representation across corporate America."