That's one of several measures that the Ontario Securities Commission is suggesting to tap an "under-represented" group of talent.
The OSC also is proposing that companies disclose how they find candidates for those positions and how they pick members of their board and high-ranking executives.
The proposals are subject to a 90-day comment period ending on April 16. The commission has already heard from the public in an earlier round of preparations for a change to corporate practices.
The recommendations released Thursday don't mention enforcing hard quotas — something some observers said was the only way to enforce change.
The Ontario Teachers' Pension Plan, for instance, had said it wanted to see at least three women on every corporate board of nine or 10 members by 2020, or have the company delisted on the exchange.
But some companies fear that if a quota system was imposed, they may be forced to promote unqualified candidates solely to meet gender requirements.
The OSC says the changes, which will work on a "comply or explain'' policy, will help bridge a gender gap in corporate Canada.
The policy means publicly-traded companies will be required to annually report their internal targets and progress — and be questioned if they refuse to comply.
"Our proposed amendments are intended to encourage more effective boards and better corporate decision making, which will benefit investors and the capital markets," said OSC chair Howard Wetston.
"This is about helping TSX-listed issuers tap into a pool of talented and capable resources currently under-represented on today's boards and senior management."