The area is a Site of Special Scientific Interest
The first excavation for decades is set to take place at one of Britain's oldest scheduled ancient monuments.
The caves at Kents Cavern in Devon date back more than 500,000 years.
If permission is granted by the Department for Culture, Media and Sport, a trial trench will be dug at the Torquay site in September.
Scientists will be looking for 40,000-year-old hand-axes, from which they hope to extract DNA to prove they were used by Neanderthal man.
In 1927, a fragment of jawbone of a young girl was excavated at the caves. Its significance was not known until recently, when scientists dated it at between 37,000 and 40,000 years old - much older than previously thought.
It prompted speculation that it might have been Neanderthal, and not from a modern human.
However, scientists were unable to extract a DNA sample, which is why a team of archaeologists wants to do some fresh digging at the caves.
Kents Cavern owner Nick Powe said: "You've got to have a very good reason to dig up a scheduled ancient monument, but we think it's so important to learn more about who lived here during this era."
"These scientists are from the universities at Durham and Sheffield and they are the leading Stone Age scientists in the country," said Mr Powe.
"We'd like to dig up an area of the caves to look for leaf-pointed hand-axes. These are commonly associated with modern humans - the scientists have technology to extract DNA from hand-axes if they are in situ and haven't been touched.
"If they manage to do that, and the hand-axes turn out to be Neanderthal, then it means they were here a lot more recently than we thought and maybe co-habited with modern humans."
The hillside, woodlands and the internal landscape of the caves are designated a Site of Special Scientific Interest under the statutory regulations of English Nature.
If the search gets the go-ahead it will be part of the guided tours at Kents Cavern during that week so the public can watch.
The scientists then plan to return for a follow-up dig 12 months later.