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.
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.