Speaking at a Women 1st event in central London this week, White said six years ago she was "absolutely anti-quotas" but has now begun to change her mind.
"I thought in the rush to make the numbers, women who were not best qualified may get appointed, but if you look at the statistics, over 60% of our graduates are women," White said.
"If we had a vote on whether we should have a quota, I would vote for it. I know it's controversial and it's not a view widely shared, but at this point, progress has not been good enough and quotas would be a way of ensuring everyone takes responsibility."
In 2011, a report by Lord Davies recommended all FTSE 100 companies have 25% female representation on their boards by 2015.
However, figures published in May 2013 by professional boards forum Boardwatch, which tracks the appointments of women to UK boards, showed the rate of appointments had slowed to 17%.
Davies said if the UK doesn't reach its target by 2015 then quotas could be introduced.
Change of views
Also speaking at the event was Lynne Franks, women's issues advocate and patron for Women 1st.
She said she had also changed her view on the controversial issue.
"I was at the original breakfast meeting chaired by Lord Davies and, when he talked about quotas, none of us thought it was necessary," said Franks.
"Since then, there has been a huge amount of work on getting more women into leadership roles, but the reality is, they're not there. So, my view has shifted and I am very keen on having quotas for as long as it's necessary until we get to that point."
Women 1st is an initiative that aims to increase the number of women in senior roles in hospitality, passenger transport, and travel and tourism.
It has set up a poll on its LinkedIn page, which allows people to share their views on whether introducing quotas would be a good move.
