This was a recommendation in Lord Davies' report, Women on Boards, which was published in February this year.
Views are also sought on whether the code should identify some of the key issues to be considered when boards carry out their regular effectiveness reviews, and on the timing of any changes that might be made to the code as a result of the consultation.
FRC chairman Baroness Hogg said: "Board diversity and effectiveness are closely linked. Diversity widens the perspectives brought to bear on decision-making, avoids too great a similarity of attitude and helps companies understand their customers and workforces. A board with too few women on it risks a weakness in at least one of these respects.
"It was these concerns that led us to add a reference to the benefits of diversity in general, with specific reference to gender, when the UK Corporate Governance Code was updated last year. But, as Lord Davies noted in his report, the rate of change in recent years has been glacial. That is why we are now responding to his proposal that boards should report on their gender diversity policy by consulting on whether it would be appropriate to add this to the Code."
Commenting on the announcement, Matthew Fell, CBI director for competitive markets, said: "We have been calling for action to get more women on boards, and believe that encouraging companies to report on their progress is the best way to achieve this.
"In our submission to Lord Davies' review, we said firms should report against internally-set targets, which reflect their different circumstances. It is good news that the FRC is proposing to follow this approach.
"Given the slow progress on improving boardroom diversity, the FRC should implement changes to the Corporate Governance Code sooner rather than later.
"With this issue under the spotlight in Brussels, the UK Government must mount a strong case for a 'comply or explain' approach to reporting, rather than imposed quotas, to promote diversity."
The consultation closes on 29 July 2011. A decision on whether to amend the Code and, if so, the timetable for doing so, will be announced later in the year.
