A bill highlighting corporate boards’ lack of women has the potential to appeal to both sides of the aisle as a House committee prepares to vote on it this week.

Legislation from Rep. Carolyn Maloney (D-N.Y.) would require publicly traded companies to disclose the gender of their directors, with the goal of nudging companies to bring more women into their mostly male boardrooms. The bill (H.R. 1611) is slated to be marked up July 11 by the House Financial Services Committee.

It’s one of only about a dozen bills put forward by Democrats, among hundreds that are filed,...