Scottish Natural Heritage (SNH) research suggested that, with suitable conditions, up to 16 breeding golden eagle pairs could inhabit the south, with more in northern England.
At present, there are just one or two pairs attempting to breed in Galloway, and between one and three pairs attempting to breed in the Scottish Borders.
The report found southern Scotland could support between 11 and 16 pairs.
As a whole, the Scottish golden eagle population numbers 440 pairs, mainly in the Highlands and Islands.
The study has presented a novel approach in which each of the nine principal regions is assessed for habitat suitability.
It explored several factors, including rainfall, plant growing, potential recreational pressure, persecution records, wind-farm developments, nest sites and woodland cover.
Professor Des Thompson of SNH, who chairs the project group, suggested the next step would involve monitoring the ranges for any golden eagle activity and developing work to improve habitats.
He said: “We would like to see on-the-ground, practical work to improve the habitat for golden eagles in south Scotland.
“With habitat improvements, we could see connections with the small reintroduced population in Ireland. This would help both groups of eagles, and could help bolster the population in north England. The approach is novel, and could work well for other regions and species.”
Environment minister Paul Wheelhouse, who lives in the Borders, said: “This offers tremendous opportunities for wildlife tourism and the prospect of re-establishing a special population of these birds.
“I’m especially pleased to see so many partners have worked together on this project.
“We will work hard to ensure that they are given the best possible chance to expand their population and range in the south of Scotland, given the region contains habitat that we would expect to sustain a greater population of this most magnificent bird.”
There have been warnings that illegal persecution continues to threaten the golden eagle population.
Ian Thomson, RSPB Scotland’s head of investigations, said: “The poisoning, trapping and shooting of these birds, and other species, simply must stop.”
Duncan Orr-Ewing, RSPB Scotland head of species and land management, said: “These magnificent birds should be given every opportunity to recover and re-occupy lost range, and must be protected in practice from the effects of human persecution, which remains a significant threat to this species.
“We need more work now to create conditions for re-colonisation by golden eagles, including a reduction in illegal killing, targeted habitat improvements to benefit existing pairs and sites with high potential for occupation, as well as a thorough appraisal of the feasibility of translocation as a tool to speed recovery.”
The golden eagle is the UK’s second largest bird of prey and has a wing span of about two metres. It was voted the nation’s favourite species by the public last year in the Year of Natural Scotland’s Big Five contest.