Martin Hymers, 34, and Michelle Hickman, 33, from Heaton Chapel, Gtr Manchester, are applying to transfer the embryos abroad.
Under UK law embryos created for surrogacy must be destroyed after five years have elapsed.
The clinic storing the embryos said it would keep them until they could be transferred to another country.
Surrogate search
The couple undertook IVF treatment following a post pregnancy hysterectomy.
They are being helped by private clinic Manchester Fertility Services to apply to the Human Fertilisation and Embryology Authority (HFEA) for a licence to transfer the embryos abroad.
The couple hope to find a woman to be a host surrogate - someone who will carry an embryo from Michelle's eggs fertilised by her husband's sperm.
This is unlike other surrogacy arrangements where a woman will have a baby for a woman who cannot produce her own eggs.
Fertility treatment
The couple admitted the search has its problems.
"There does not appear to be a list of countries where host surrogacy is legal for us to use as a starting point," they said.
"We know it is illegal in Spain and Sweden. We know it is legal in America however we would prefer something closer if possible."
The couple, who spent £10,000 on fertility treatment, are yet to find a host surrogate mother and have seven other embryos which are due to be disposed of next year.
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