Energy Minister Fergus Ewing refused permission for the 21-turbine Rowantree development near Oxton last May.
He said the decision was based on "unacceptable environmental impacts".
RWE Innogy UK has submitted scoping plans to Scottish Borders Council for a wind farm of up to 11 turbines in the same location.
The proposed development on land north-east and east of Burnhouse Mains farmhouse, between Stow and Fountainhall, will be known as Longmuir Rigg wind farm.
A letter lodged with the council states that RWE's new plans for the site take into account the Scottish government's concerns about the Rowantree development.
In the correspondence, project manager Christopher McPake states: "It has sought to reduce or negate the identified significant environmental effects of cumulative noise as well as effects upon landscape character and visual receptors."
It lays out plans to build between nine and 11 turbines, no more than 130m (426ft) high.

Police Scotland said they had searched four properties and had seized drugs worth about Â£65,000 and a four-figure sum of cash.
An air weapon was also recovered during the operation. The drugs seized are believed to be cocaine.
Three men, aged 65, 38 and 18, and two women, aged 68 and 39, were arrested for alleged drugs offences.
They are expected to appear at Paisley Sheriff Court on Monday.
A 64 year-old woman and a 66 year-old man will also be subject of a report to the procurator fiscal in connection with the air weapon.
Officers said they had searched homes in Cameron Avenue in Bishopton, Ryat Linn and Sconser in Erskine, and Merlinford Crescent in Renfrew at about 15:30 on Friday.

The beavers were temporarily captured for testing from the River Otter in Devon, where they have been living wild for at least three years.
Tests revealed they were free of bovine TB and a parasitic tapeworm.
Devon Wildlife Trust said it was "delighted" the animals had returned to the river.
DNA tests also confirmed the animals were Eurasian beavers, a species found in the UK before being hunted to extinction several hundred years ago, rather than North American beavers.
Evidence emerged in 2014 they had produced young, known as kits, and ministers said they intended to trap the beavers, test them for disease and rehome them in captivity.
The move was opposed by wildlife experts, who put forward plans for a five-year trial monitoring them in the wild, with the support of local people, and Natural England, who gave the scheme the go-ahead subject to the mammals being found clear of disease.
The five beavers - two adult pairs and one kit - have been temporarily homed in captivity in Devon with access to water and artificial lodges.
Devon Wildlife Trust's Peter Burgess said: "Today's re-release means that these beavers are back where they belong, in the wild on the River Otter.
"We're delighted and relieved they've coped very well with a short period in captivity and have been given a clean bill of health.
"They've tested free of serious infectious diseases and we're now looking forward to starting the next phase of our work: studying the long-term effects of these wild beavers on the local landscape, on local communities and local wildlife."
Plans have been lodged for a wind farm in the Scottish Borders less than a year after the Scottish government rejected a scheme for the same site.
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Five people have been arrested after a series of drugs raids at homes across Renfrewshire.
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The only wild beavers in England have been released back into their river home after being given a clean bill of health.