"The public do not like, and we do not like the idea of designer babies," she said. Mrs Deech added that the HFEA did not deal with individuals, only clinics.
Alan and Louise Masterton spoke out after a statement by the head of the Human Fertility and Embryology Authority (HFEA), who said that the the rules would not be changed to accede to their wishes.
The Mastertons have been seeking to have a girl after they lost their only daughter Nicole following a bonfire accident.
In an interview on BBC Newsnight Scotland, HFEA chairwoman Ruth Deech made it clear the rules would not be relaxed for fear of setting a precedent.
Under the present guidelines couples can only select a child's sex if there is a pressing medical reason, such as a risk of the baby inheriting a serious genetic illness.
Mrs Deech said: "I do not want to give an opinion on one case, but obviously we always take into account precedent.
"If we give one clinic a licence to carry out a brand new treatment it would be difficult for us to refuse a licence to another clinic to carry it out again."
Mrs Deech said the current policy was the result of consultation with the public.
"The public do not like, and we do not like the idea of designer babies," she said. Mrs Deech added that the HFEA did not deal with individuals, only clinics.
The Mastertons said clinics were "highly unlikely" to make applications which flew in the face of the association's guidelines.
The couple said that this statement contradicted a letter received from Suzanne McCarthy, the chief executive of the HFEA, last October.
They said Mrs McCarthy told them to submit all the information they wanted to put before the authority.
'Respect for life'
This led them to believe that they would be given a fair hearing for a change in the rules.
The couple intend to raise a legal action, claiming that their human rights have been breached.
They contend that the HFEA has denied them a fair hearing and that the authority's behaviour breaches their right to "respect for private and family life".
A spokesman for the HFEA said they had agreed to a general television interview about the issue of gender selection but claimed that Newsnight Scotland had "jumped the gun".
The licence committee of the HFEA could consider an application, he said.
"They could still go to a clinic and get them to make an application as before. The licence committee can and has made exceptions in the past."
Mr Masterton said: "As I have said many times before, if some other family think they have a strong enough case to present to the HFEA for a designer baby then let them make that case at that time.
"That is not the objective of our application or indeed what we desire as a family."
Selective destruction
The Mastertons have asked to use a technique known as pre-implantation genetic diagnosis (PGD) as part of the standard IVF process.
This involves the selective destruction of male embryos and is usually employed for families with a history of hereditary diseases in male children, like haemophilia or muscular dystrophy.
Dr Simon Fishel, director of the Centre for Assisted Reproduction, admitted that the case fell into an ethical grey area.
He said: "I would personally, in this particular circumstance, carry the treatment out.
"But I would have to go to the clinic and our ethics committee, and I know that our ethics committee would not make a decision because it is not up to the ethics committee to make a precedent for the HFEA."