Christian charity Care has approached the local authority asking for assurances that the law was not broken when the grandparents' protests were over-ruled.
The grandparents have reportedly now lodged a formal complaint about the actions of social work staff in a first step towards overturning the adoption. They claim they were pressured into giving up their carers' rights and their wishes ignored. The council is legally obliged to consider the family's views before deciding who should bring up the children.
Social work leaders insist they did take the grandparents' feelings into account before deciding where to place the children.
The grandparents say they were told they must change their attitude and support the decision to place the children with a gay couple or never see the five-year-old boy and four-year-old girl again.
Gordon Macdonald, spokesman for Care, said: "We obviously don't know all of the details of this case but I personally believe that the allegations are of such a serious nature that it merits further investigation.
"The Adoption Act requires the views of both relatives and the children to be taken into account and we need to be satisfied that has happened here."
Social workers fear the adoption may fall through following the row over the decision. They are worried the gay couple and the children may face abuse if their identities become known.
But council leaders have insisted they stand by the policies they have followed and the way they have been implemented.
City education leader, Councillor Marilyne MacLaren, said: "The care of children has never been more regulated or under such close scrutiny. Not only is there national legislation which covers our duties and responsibilities, but we have well-established policies that we stand by.
"These are difficult decisions but we are confident we made the right decision and have no reason to doubt the staff involved acted with anything other than professionalism and sensitivity."
Today, the Tories attacked the decision to rule out an inquiry.
The city's Conservative spokesman for children and families, Councillor Jeremy Balfour, said: "There are still a lot of issues that have to be clarified and we need the reassurance that this is being dealt with comprehensively.
I have a couple of concerns.
"Firstly, how the grandparents have been treated but also the alleged phone conversations where they were told they would never see the children again because of their objections.
"This goes to the heart of the council's adoption policy and we need to be confident that the system is fair and transparent."
The grandparents, who are believed to live in the south of Edinburgh, have said they are not homophobic, but believe the children would be better off with a mother as well as a father.
It is reported that there have been at least ten other gay adoptions in Scotland over the last five years.