EU Justice Commissioner Viviane Reding will then present an altered proposal after failing to gain sufficient support. She tweeted after the initial discussions that she will not give up in her quest to make gender quotas mandatory.
The debate originated from criticism from the European Parliament over the number of female candidates for the Central Bank.
If the proposals are agreed upon, the European Parliament will vote to make gender quotas mandatory across the 27 countries in the European Union. According to the Commission, women currently hold currently less than 15% of EU board positions.
Several major European countries, including France, Spain and Italy, introduced quota laws. However, the UK has strongly opposed the plans.
Although most countries agree that more should be done to increase the number of women in upper management positions, those opposed to the Reding plan argue that Brussels should not meddle with domestic gender related issues.
Jo Swinson, the new employment minister, recently voiced concerns that the quotas could lead to poor quality female candidates.
Last month Dame Marjorie Scardino, the first female head of a FTSE 100 company, resigned from her role at Pearson, leaving just three female chief executives at the UK's 100 biggest quoted companies - Angela Ahrendts at Burberry, Cynthia Carroll at Anglo American and Alison Cooper of Imperial Tobacco.
Kate Swann left WHSmith after nine years at the helm last month.