The couple, who haven't been named, were told by social services their comment that children need both a "mummy and daddy" was "concerning".
After the council ruled allowing them to adopt their two foster children could be "detrimental to the long-term needs of the children", the couple - who already have two adopted children - have asked the authority to review its decision.
The Christian Legal Centre has been supporting the couple, who have been providing foster care for the two children since the beginning of the year.
On Tuesday council officials met to discuss the case.
The foster mother told the BBC's Victoria Derbyshire programme: "We can't imagine [the children] being under the care of two men.
"As a girl or a boy, you're looking for a model. And, for us, the best parenting model is [a] mum and dad."
She added: "The [same-sex couple] are probably lovely and want to be parents and may have more money, but I feel that we've been discriminated against because of our religion.
"There is no free speech because if I'm [talking about something] that's better for my family, or my life, and it's not hurtful to anybody, why shouldn't I say that?"
The council confirmed a review would take place but refused to comment further.
