The Old Tweed Bridge was opened by Sir Walter Scott in 1832 and it was the main link between Selkirk and Galashiels for 140 years.
However it fell into a state of disrepair following the opening of the nearby A7 crossing of the river.
Transport Scotland has submitted plans to Scottish Borders Council to carry out extensive repairs to the bridge.
In its proposal to the local authority, the roads agency claimed the bridge, was "structurally unsound".
It once carried the old A7 but now only pedestrians and cyclists can use the bridge.
Transport Scotland wants to remove the spandrel walls to build a new concrete saddle over the arches before rebuilding the structure.
Plans have been drawn up to repair an historic bridge which links two Borders towns.