The current law allows single gays and lesbians to adopt, but bans de facto and gay couples because they are unmarried.
Green MP Metiria Turei has drafted a member's bill to allow gay and lesbian couples to adopt.
However the bill is sitting in Parliament's ballot, where only a small proportion of member's bills are drawn and introduced to the House.
Cabinet Minister Chris Carter, who is gay, told today's New Zealand Herald the Government was considering its position in relation to the bill and "talking about" whether it should introduce its own legislation.
A spokesman for Mr Burton today said officials were looking at options for updating several aspects of adoption law.
But he and Prime Minister Helen Clark's office were at pains to point out that gay adoption was not a specific term of reference for officials' work, nor was introducing legislation on the Government's agenda.
In the last term the Government took a lot of heat from conservative sections of the community over the Prostitution Reform Act and the Civil Union Act even though it was not directly responsible.
The former was a member's bill of Labour MP Tim Barnett but was passed by a conscience vote.
The latter was adopted by the Government but was also passed by a conscience vote.
That did not stop sections of the public associating both bills with the Government, which suffered a backlash as a result.
That has created high sensitivity over other social change legislation that might give conservative opponents a platform to label the Government politically correct.
Mr Burton's spokesman today said the areas officials would look at were:
pre- and post-adoption support services;
recognition of overseas adoption; and
who is eligible to adopt.
Once the work was completed options would be presented to Cabinet.
Ms Turei has said the wording of current adoption laws is hopelessly outdated and discriminatory.
Her Adoption (Equity) Amendment Bill was a chance to fill a major hole in the law.
"In some ways it's a very small legislative hole but it has big impacts for gay and lesbian couples and there's no policy reason at all why it shouldn't be filled. It's just none of the other political parties have had the gumption to do it."
Mr Carter said he was personally in favour of the bill.