Church, who heads the Harvard Woolly Mammoth Revival team, said: "We're working on ways to evaluate the impact of all these edits and trying to establish embryogenesis.
"The list of edits affects things that contribute to the success of elephants in cold environments," he said. "We already know about those to do with small ears, subcutaneous fat, hair and blood, but there are others that seem to be positively selected."
He added: "Our aim is to produce a hybrid elephant-mammoth embryo. Actually it would be more like an elephant with a number of mammoth traits. We're not there yet, but it could happen in a couple of years."
The woolly mammoth, which is most closely related to the Asian, rather than African elephant, roamed Europe, Asia, Africa and North America during the last Ice Age and vanished some 4500 years ago, probably due to a climate change and hunting by humans.
"De-extinction" has become a realistic prospect due to revolutionary gene editing techniques that allow precise selection and insertion of DNA taken from specimens found in Siberian ice.
Church helped develop the most widely used technique, which is known as CRISPR/Cas9, that has transformed genetic engineering since it was first demonstrated in 2012. It derives from a defence system bacteria used to fend off viruses and allows precise "cut and paste" manipulation of strands of DNA.
Dr Edze Westra, of the University of Exeter, said Church's work "represents a massive opportunity", but he added: "I'm not sure if it is something we should be doing now, but it is definitely something that the technology offers."
Some experts argue that the technology should be used to save animals that are still alive but in decline, rather than trying to bring back extinct creatures.
Dr Beth Shapiro, author of How to Clone a Mammoth, said scientists would never achieve a creature that was "100 per cent mammoth". She added: "Elephants are an endangered species, and what if you could swap out a few genes for mammoth genes, not to bring the mammoth back but to allow them to live in colder climates."
Church said the mammoth project had two goals; to secure an alternative future for the Asian elephant and to combat global warming. "They keep the tundra from thawing by punching through snow and allowing cold air to come in," said Church. "In the summer they knock down trees and help the grass grow."