Pte Cheryl James, 18, from Llangollen, Denbighshire, was found with a bullet wound to her head in Surrey in 1995.
Her parents said a dispute over the ballistics evidence could only be resolved if her body is exhumed.
Coroner Brian Barker QC said he would wait for a doctor's report before he made the decision.
He told the pre-inquest review at Woking Coroner's Court that exhumation was a "difficult and unusual" step.
Alison Foster QC, representing Pte James' family, said her relatives were "really dismayed to be at this point today".
"From our standpoint, an exhumation would be necessary for you to carry out a full and proper inquiry."
Bullet fragments in Pte James' body were yellow, while the SA80 rifle she was armed with used red bullets, Ms Foster said.
"There is no actual evidence that it was an SA80 that caused the bullet wound to Cheryl," she added.
The coroner said the full inquest on 1 February would consider whether there were "shortcomings" with the barracks's policies on sexual behaviour, supervision of young females, drugs, alcohol and accommodation.
Another pre-inquest hearing is to held on 10 September.
Pte James was one of four soldiers found dead at Deepcut, in Camberley, between 1995 and 2002.
Surrey Police's request that her inquest should be heard alongside fresh inquests into the deaths of Privates Sean Benton, Geoff Gray and James Collinson was turned down.
A spokeswoman for the force said: "[Surrey Police] has now completed the review of disclosure documents relating to Pte James."
She said arrangements for the inquest were a matter for the coroner.
"Surrey Police is supportive of the view that there should be a thorough inquest into circumstances surrounding the death of Pte James and our thoughts remain with her family."

It says "cosmetic lightening and hygiene creams... that de-pigment the skin... are now forbidden".
Whitening creams have been popular for years among young women - and some men - across Africa, who believe they make them more beautiful.
But medical experts say they may cause cancer, diabetes, severe skin conditions and other diseases.
"The number of people with side-effects caused by these medicines is really high," Christian Doudouko, a member of Ivory Coast's pharmaceutical authority, was quoted as saying by the AFP news agency.
Latest African news updates
Africa: Where black is not really beautiful
British consultant dermatologist Justine Kluk told the BBC the major concern was over unregulated products, which may contain ingredients such as mercury or excessive amounts of steroids.
"If one thinks about steroids being present in these products, they're often present in much higher quantities than we would prescribe," she said.
She said the creams can cause a variety of health issues, such as "acne, thinning of the skin, glaucoma or cataracts if applied near the eyes".
"Or if applied liberally to the whole body, [they can] cause high blood pressure, diabetes, osteoporosis, weight gain, mood disturbance due to absorption of large amounts of steroids," she said.
However, analysts say the ban may not stop people buying the products.
They are still used in The Gambia despite a ban.
South Africa has the world's toughest laws against skin lighteners, having prohibited the most active ingredient - hydroquinone, but a University of Cape Town study found that more than a third of South African women still buy them.
The use of whitening creams in Africa is most widespread in Nigeria - where more than 75% of women buy them, according to a 2008 UN Environment Programme study.
The family of a soldier found dead at Deepcut Barracks has urged a coroner to let her body be exhumed so a "full inquiry" can be held into her death.
[NEXT_CONCEPT]
Ivory Coast has banned skin-whitening creams because of health concerns, the health ministry says.