The anonymous couple were told by social services that their request will not be considered because of their "concerning" opinions on same-sex parents.
The Christian Legal Centre is supporting the couple and Andrea Williams, chief executive, told Premier the parents had previously asked to adopt but had been told their home was too small.
"They accepted that the social working was telling them that," she said.
Andrea Williams went on to say that the parents had been keen to adopt the children.
"They said immediately we want to look after them, we want to adopt them, we love them, they're thriving in our care, they're thriving with a mum and a dad and this is not the situation we want for them, we believe the best interest of the child will be served if they stay with us."
The couple have written to their local council, seen by The Sunday Times, saying they had "not expressed homophobic views, unless Christian beliefs are, by definition, homophobic."
Their letter went on: "We are Christians and we expressed the view that a child needs a mother and father."
"We love everyone (regardless of sexual orientation) and we love the children and believe that they would benefit from the foundation offered by a mother and a father," it said.
The case came to light after a gay couple was put forward to adopt the foster children, the Christian foster carers "expressed a degree of shock and asked if this was a 'joke'," according to their letter.
After the male couple applied to adopt the children, they put in a request to adopt them as well.
The council told the couple that their opinions were "concerning" and could be "detrimental to the long-term needs of children."
Listen to Premier's Hannah Tooley speak to Andrea Williams here: