The parents are believed to be the first from this country to use the method, which is being offered by the IVF Institute in Fairfax, Virginia. They are understood to have tried the treatment because they already have three sons and wanted a daughter. A scan has confirmed that the woman, who is in her thirties, is carrying a girl.
The IVF Institute published a report in the journal Human Reproduction last week, claiming an 85 per cent success rate for selecting girls and 65 per cent for boys, through its MicroSort technique.
The clinic sorts sperm by staining it with a fluorescent dye which helps distinguish between male- and female-producing sperm.
The only other reliable method of sex selection available for parents who want to choose the gender of their child is through in vitro fertilisation treatment (IVF). However, this was banned in Britain four years ago, except for couples who have a history of genetic diseases, such as haemophilia, which is inherited only by male babies.
There are other methods of sperm-sorting offered by clinics in this country, but there is little scientific evidence to prove that they are reliable.
The couple was referred to the IVF Institute by the London Gender Clinic because its own method had a poor success rate in selecting female babies.
Dr Peter Liu, director of the London Gender Clinic, said it was possible that the MicroSort method could be adopted in this country.
"They are the first people we have sent because there is no one providing the MicroSort method in this country and other methods are not as reliable," he said.
"The couple have three boys and wanted a girl to complete the family. The initial results show it's working well for the clinic but there is still a lot of work to be done to ensure its efficiency. We have already had quite a lot of interest."
However, the treatment was condemned by the Human Fertilisation and Embryology Authority on ethical grounds.
A spokesman said: "Until recently, the only method of sex selection was through IVF treatment, which is a very reliable method but was banned for anything other than medical reasons four years ago.
"There is very little medical evidence that the other treatments work and we think it is unacceptable to determine the sex of your child unless there is a medical reason.
"What message are you putting across to your other children if, for example, you have all boys and want a girl? There are a lot of complex psychological reasons why gender selection should not be allowed. We would have to take legal advice if a licensed clinic approached us in this country wanting to adopt this treatment."Reuse content