Archaeology Scotland (AS) believes the remains of a military settlement, thought to date from the second century AD, lies somewhere beneath the areas of Fairmilehead and neighbouring Buckstone in the south of the city.
About 50 residents have been asked to grant archaeologists access to their gardens next month for a test dig which historians hope will uncover a nationally significant find.
The site is thought to be a missing link in a chain of camps Roman soldiers used as they marched across the country about 1800 years ago.
AS development manager Dianne Laing said: "We're looking for about 50 householders to make their gardens available.
"The evidence for a camp is there but we don't yet know exactly where it is located."
The AS researchers concluded there were probably remains in the area after examining four different maps, including one dating back to the 1760s.
She continued: "There are four different maps showing what we think is a camp in slightly different locations.
"What we can see from three of the maps is some kind of rectilinear embankment, which makes us think it is Roman.
"But one of the maps show the embankment as oval, which could mean it dates from the Bronze or Iron Age."
Ms Laing said any finds would be a treasure trove for researchers, adding: "We might find weapons and there are likely to be bits of pottery.
"We could find Samian-ware, which is a distinctive, bright red Roman pottery that was only in use for a short period of time and was made in what was called Gaul, now France."
Ms Laing said she and her colleagues were also excited by the prospect of pieces of Roman armour being discovered too.
Lesley McEwan, national co-ordinator for Archaeology Month, said: "It's a possible way-station for Roman soldiers on their way somewhere else.
"The camps are spaced out at about a day's march, and there is a gap where we think this one is."
Roman legions were in Scotland in three separate periods. They stayed for only a few years before withdrawing in the first century AD.
In the second century they stayed from 138AD to 160AD, and returned in 208AD for a campaign that ended four years later.
During the second, longest occupation they built two important bases at Inveresk and Cramond. The Cramond fort would have housed up to 1000 legionnaires.
Richard Lewis, Edinburgh council's culture and sport leader, said: "This is a unique opportunity for local people in the Fairmilehead and Buckstone area to get involved in archaeology and perhaps make that all-important discovery that would rewrite the history of Edinburgh."