Speaking at the AAAS annual meeting in Austin, Dr Hiro Nakuachi, who is leading the research, said he believed that organs grown in animals will be available for transplant within the next five to ten years.
"We have already generated a mouse pancreas in rats and then transplanted those in to diabetic mouse and were able to show almost a complete cure without any immunosuppressants," he said.
"When it comes to human-sheep it seems more difficult. So we would like to proceed a little longer and this time use organ-deficient embryos.
"It could take five years or it could take 10 years but I think eventually we will be able to do this."
Britain is currently facing a transplant shortage crisis because medicine has advanced to such a degree that many more lives are being saved, so there are fewer donor organs available.
Last year, researchers from The Salk Institute in the US created human-pig hybrids but no lab has yet succeeded in growing an organ. In the pig experiments researchers created embryos where one in 100,000 cells were human, but the new study has increase human cells to one in 10,000.
Previously scientists had hoped that pig or sheep organs could be used directly because they are roughly the same size as a human. However they were always rejected. The new approach gets round the rejection problem because it uses stem cells directly from a human patient.
Sheep also have similar heart and lungs to humans, and their embryos have previously been shown to form chimeras with goat embryos, creating geeps. The process is also more efficient than in pigs. Transplanting around 40 to 50 embryos into pig surrogates only leads to up to 14 piglets, while transferring three to four sheep embryos brings yields of up to three fetuses.
Dr Pablo Ross, who works with Dr Nakauchi added: "The sheep is a good model for many human conditions.
"The size of the sheep organs is similar to human size, some of the organs are physiologically similar between sheep and humans and a lot of cardiovascular research is done in sheep because it has some similarities to humans in terms of heart shape."
To make the hybrids scientists transplanted human stem cells into preimplantation embryos of sheep. The embryos were allowed to grow for a week before being implanted into a surrogate sheep. Current rules ban labs from allowing the survival of hybrids beyond 21 days, so the surrogate animal was slaughtered after three weeks.
British scientists said it would be groundbreaking if the team managed to grow an organ inside an animal.
Professor Ludovic Vallier at the Wellcome – MRC Cambridge Stem Cell Institute said: "It would definitely be a world first if Hiro could demonstrate that he can generate a human organ in the sheep."
However Robin Lovell-Badge, of the Francis Crick Institute in London, warned the resulting organs may still be rejected by the body.
"Even if they succeed in replacing all pancreatic cell types in the sheep with human cells, the blood vessels within the pancreas will be sheep derived," he warned.
"The organs could not be used for transplants into humans without triggering the immune system to reject them – and this would probably be a very fast rejection."