Scientists want to test human embryos
The Roslin Institute, near Edinburgh, will apply to the UK Government's fertility authority for a licence within the next couple of months.
They want to investigate ways of harvesting human stem cells which are found in the growing embryo.
Experts believe stem cells have the potential to treat degenerative diseases such as Parkinson's and Alzheimer's.
The Roslin Institute is also considering how it could apply its technique, cell nuclear replacement, to human embryos.
The scientists propose establishing methods for deriving human embryonic stem cells by using surplus embryos - or embryos created specifically for the purpose by IVF.
Professor Ian Wilmut, head of the institute's gene expression and development division, said: "We will be applying to the Human Fertilisation and Embryology Authority for a licence within the next couple of months.
"It is a significant shift for us and a natural way to go."
Prof Wilmut said the Human Fertilisation and Embryology Authority may take up to three months to decide on the application.
Dolly was the first mammal to be cloned from an adult cell and came into the world in 1996.
In January, Prof Wilmut confirmed that Dolly had arthritis. He said the condition may have arisen because of genetic defects caused by the cloning process.